My take on the "Stand user" subclass and stand physics, gaining inspiration from the various other homebrew stand user subclasses on dndbeyond. This subclass aims to provide a template to create stands unique to your character, giving ideas and options to get creative with the various gimmicks stands have.

A stand is a physical manifestation of your will and fighting spirit, appearing as a ghostly, incorporeal figure with an appearance of your choice. Either by being born or blessed with it or from interacting with a special arrow (called a stand arrow), you gained a stand that until now has remained dormant within your body. Through your training, you have awakened your stand from this dormant state and can now bring it out to help you in battle for a short amount of time. Stands are invisible to all except you and other stand users, and each stand has a unique ability that they can use. Your stand gets more powerful as you level up in this class, gaining better/more abilities, becoming stronger and more active, finally evolving into its most powerful form, a requiem stand. Stand users are also strangely attracted to each other, so expect for you to meet many other stand-wielding enemies and allies on your adventures.

Awakened Stand

Your stand has awakened, allowing you to summon and control it for a short period to help you. As a bonus action, you can spend 1 ki point to activate your stand, which appears in an unoccupied space within 10 feet of you. Every minute (10 rounds), you must expend 1 additional ki point to keep your stand active or have it deactivate. You may also deactivate the stand of your own volition at any time, requiring no action. If you are incapacitated or die, your stand also disappears.

Your stand is a creature or swarm of any size retaining everything on your character sheet (stats, proficiencies, features and traits, etc) except for your equipment and hp (see damage and effects section below), with a hover speed equal to your walking speed. Stands appear translucent to you, other stand users, and creatures who can see invisibility, but are completely invisible to all others. You can expend your action to take control of your stand, perceiving through its senses, taking its actions, and moving it up to its speed. Otherwise, your stand will remain stationary and actionless. You may also use any ki or class/racial features that you have such as flurry of blows when taking control of your stand. 

Attacks. For your stand's base attack, you can choose between melee and ranged. A melee stand follows the same rules as you, being able to make an additional unarmed strike after taking the attack action with a weapon it is proficient with. Ranged stand attacks have a range of 30/120 and fire an incorporeal projectile that deals damage equal to your unarmed strike. However, they cannot make an extra attack as a bonus action. You can decide which damage type your stand's attack deals, but it counts as magical damage for the purposes of overcoming resistances.

Damage and Effects. Your stand does not have hit points. Instead, all damage done to your stand is directly done to you. This goes the other way as well; if your stand is targetted by a healing effect, you gain the benefits. Your stand is still subject to any non-damage effects (like conditions), with all effects applied to your stand also applying to you and vice versa. If both you and your stand are subjected to the same effect at the same time, like from an area of effect spell, you take only one instance of the damage and/or effect, not double. If the effect requires a saving throw, you gain the benefits of a success even if only one of you succeeds on the save.

Range. Your stand also weakens as it travels farther from you. It is most effective while it is within 30 feet of you, having access to all your abilities. After your stand leaves this area but is still within 120 feet, it may only take an action or a bonus action, not both, and cannot take reactions. Beyond even that distance, it cannot take any actions or reactions. However, you can use your stand ability at any range, making actions/bonus actions/reactions if applicable, and you may still use your action to control and perceive through it.

Ephemeral. Your stand can't wear or carry anything but is unable to pass through solid objects and creatures. It can, however, affect things in its environment, for example pulling levers, making checks to push objects, etc. Your stand does not require air, food, drink, or sleep. 

Stand Ability

Your stand has also developed a special ability, a unique perk or skill that provides additional power and utility to your stand. You gain one stand ability at 3rd level and a second at 11th level. Each time, you may choose one of the abilities listed below, or speak with your DM to create a new one. Every time you hit 6th, 11th, or 17th level, you may also swap out your previous stand ability(ies) for new ones or change an existing ability's effects (ex. changing the spell your stand casts from the spellcasting stand ability). Your stand must be active for you to use its stand ability.

Spellcasting

Choose a spell from any spell list, except wish. If you chose a cantrip, then your stand now knows that cantrip and can cast it at will. If you chose a spell of 1st level or above, you must expend ki points equal to the spell's level every time your stand casts it. You can only choose spells that a full caster class would be able to cast at your level, for example at 3rd level you would only be able to choose a 1st or 2nd level spell, at 5th level, up to 3rd level spells, at 7th level, up to 4th level spells, and so on. Only your stand can cast the spell, so it must be active with you controlling it to do so. You may also upcast your spell, spending an additional 1 ki point for every level you upcast it. Wisdom is the spellcasting ability for your stand. 

Extracurricular Feature

Choose a feature/special trait from any class, subclass, race, or monster stat block that is available at your level or has a CR not higher than your level. Your stand permanently gains that feature, and if it has limited uses, you can regain all expended uses of that feature by deactivating and resummoning your stand. The feature also scales to your monk level if it gets more powerful or gains more uses at higher levels. 

Innate Magic

Choose a magic item or piece of equipment/gear. This item is now permanently part of your stand. Your stand is considered proficient with the item and bypasses any class/race restrictions it has. If the item is a consumable or has charges, it will get used up normally, but deactivating and resummoning the stand will return all expended uses of it. For special varied items like spell scrolls, you must choose its contents once (in this case the spell it holds) and only be able to alter that selection when changing stand abilities. At 3rd level, the item you choose is limited to those of common rarity, at 6th level, uncommon, at 11th level, rare, and at 17th level, very rare. If you choose a type of magical ammunition, then your stand's ranged attacks, if any, gain the benefits of the ammunition. 

Heightened Sense

Choose one sense (darkvision, blindsight, etc.). Your stand now has that sense with a range of 200 feet, and you can perceive through it whenever you take control of your stand. If you had that sense already, from a racial trait or class feature, its range increases to 400 feet.

Superior Movement

Choose a type of movement (burrowing, climbing, etc.). Your stand now has that movement type with a speed equal to twice your walking speed. If you chose a burrow speed, your stand leaves behind a small-sized tunnel as it burrows through the ground. If your character innately has the selected movement type, then your stand's speed for that movement type increases to quadruple your walking speed.

Corporealness

Your stand has become strong enough to impose more of its presence on the material world. Your stand can now be seen by non-stand users, and can now carry and wear equipment, with a separate inventory and carrying capacity of 5 times your strength score. 

Etherealness

Your stand becomes more nonmaterial, appearing even more ghostly and translucent. It is now able to move through solid objects and creatures freely but must take 5 (1d10) damage if it ends its turn inside or partially inside an object or creature.

Posthumous Stand

Many people have had their stand awaken, but were unable to control it, causing it to go rogue. Such a renegade stand is called a posthumous stand, one that is detached from its user. However, you are strong enough to control it and with this ability create a different type of posthumous stand; one that can persist after its user's death. Speak with your DM to see what is the nature of your contingency stand, whether it becomes an NPC under the DM's control or an all-new character played by you, and if it gains a new personality and agenda or follows some sort of instruction from its user.

Stand Stats

At 6th level, your stand has become more powerful and can now enhance two of its 6 special attributes; Power, Speed, Range, Durability, Precision, and Potential. You get to take one additional enhancement each time you reach 11th and 17th level. Only your stand gains these benefits.

Power

Your stand gains a +2 bonus to all damage rolls. If an attack or effect deals multiple dice of damage, such as 3d6 from a burning hands spell, the bonus is only applied to one die.

Speed (Attack)

Your stand gains an extra attack when taking the attack action, and makes 2 more attacks than normal when using the flurry of blows feature.

Speed (Movement)

Your stand's movement speed increases by 20 feet, across all movement types.

Range (Attack)

Your stand's melee attack range doubles and all its ranged attack ranges increase by a factor of 1.5. This applies to a spell's casting distance, but not the dimensions of the effect itself.

Range (Movement)

Your stand now suffers no penalty to actions and reactions at all farther distances.

Durability (Armor Class)

Your stand gains a +2 to AC.

Durability (Resistances)

Your stand gains immunity to 2 conditions, 1 damage type, or resistance to 2 damage types.

Precision

Your stand gains a +2 bonus to all attack rolls, and its save DC for spells and ki abilities increase by 2.

Potential (Proficiency)

Your stand gains proficiency in 2 additional saving throw proficiencies or 3 skills, tools, languages, or weapons/armor. You can also use any of the choices to get expertise in skills it is already proficient with.

Potential (ASI)

Your stand gains 3 additional points to improve its ability scores. You may use them in any combination, whether it be all 4 points to 1 ability score, 1 point to 4 ability scores, or something in between. With this feature, you are also able to increase your stand's ability score beyond the normal maximum of 20.

Silent Stand

At 11th level, you have grown so powerful that your stand's abilities reflect on yourself. You gain its stand stat benefits and are able to use its stand ability(ies) without having to activate your stand first.

Requiem Ability

Your stand has evolved into a drastically more powerful form, called a requiem stand. The effects of all its stand stat enhancements double, and it gains a powerful new ability based on your strongest desire at the moment of first use. Upon first use of this ability, which costs 16 ki points, you may cast the wish spell without the 33% chance of not being able to cast it again. Any subsequent uses of this ability will have to replicate the same effect that was chosen on your first use of this ability.