My attempt to play Spider-Man in D&D version 2. Hopefully, more in line with the subclasses released in Tasha's Caldron of Everything.

Wall Crawling

Starting when you choose this tradition at 3rd level, you gain the ability to move up, down, and across vertical surfaces and upside down along ceilings while leaving your hands free. You also gain a climbing speed equal to your walking speed. In addition, you ignore movement restrictions caused by webs and webbing and while in contact with a web, you know the exact location of any other creature in contact with the same web.

The Spider's Web

Starting when you choose this tradition at 3rd level, you can produce webbing to use in combat. When you use the Attack action, you can replace any attack you make with one of the following special ranged weapon attacks:

• An Impact Web is fired at a Huge or smaller creature within 60 feet of you. On a hit, it takes your unarmed strike damage and its speed is reduced by 10 feet until the end of your next turn.
• A Web Line is fired at a Huge or smaller creature within 20 feet of you. On a hit, it gets pulled up to 20 feet toward you and you gain advantage on attack rolls against it until the end of your turn.
• A Web Bola is fired at a Huge or smaller creature within 30 feet of you. On a hit, it must succeed on a Dexterity saving throw or be restrained.

Spider Sense

Beginning at 6th level, your Spider Sense grants you advantage on Dexterity saving throws.

Improved Webbing

Beginning at 6th level, as an action, you can spend 3 ki points to gain the ability to cast the web spell without requiring concentration at will for 1 minute. Any webs conjured in this way disappear after 1 hour.

Does Whatever A Spider Can

Beginning at 11th level, you gain Expertise in the Perception and Acrobatics skills.

Spacial Awareness

Beginning at 11th level, you gain a +10 bonus to your Passive Perception. You also can't be surprised.

Improved Spider's Web

At 17th level, the special ranged weapon attacks granted by your The Spider's Web feature now effect Gargantuan or smaller creatures.

Improved Spider Sense

Beginning at 17th level, you can use your action to spend 5 ki points to gain advantage on all saving throws and cause all attack rolls targeting you to have disadvantage for 1 minute.