Interacting with objects in combat

Hi!

My D&D group is quite confused - me included - with some rules around interacting with objects.

Here are the rules that are confusing us at the moment:

Time-Limited Object Interactions

When time is short, such as in combat, interactions with objects are limited: one free interaction per turn. That interaction must occur during a creature’s movement or action. Any additional interactions require the Utilize action, as explained in “Combat” later in this chapter.

Interacting with Things. You can interact with one object or feature of the environment for free, during either your move or action. For example, you could open a door during your move as you stride toward a foe.

If you want to interact with a second object, you need to take the Utilize action. Some magic items and other special objects always require an action to use, as stated in their descriptions.

The DM might require you to use an action for any of these activities when it needs special care or when it presents an unusual obstacle. For instance, the DM might require you to take the Utilize action to open a stuck door or turn a crank to lower a drawbridge.

Attack [Action]

When you take the Attack action, you can make one attack roll with a weapon or an Unarmed Strike.

Equipping and Unequipping Weapons. You can either equip or unequip one weapon when you make an attack as part of this action. You do so either before or after the attack. If you equip a weapon before an attack, you don’t need to use it for that attack. Equipping a weapon includes drawing it from a sheath or picking it up. Unequipping a weapon includes sheathing, stowing, or dropping it.

The first two quotes suggest that you have one free interaction with an object during your combat turn. The question is: in the third quote, does equipping or unequipping a weapon count toward that one free interaction with an object during your combat turn?

Thanks in advance! I'd appreciate an official statement about this, since we've decided to stop using homebrew rules / contents. If there are no official statements on this, then it will be up to the DM to choose how to interpret those confusing rules.

So let's imagine a fighter lvl 5.

Could he, with action surge and extra attack, do the following?

1) Draw his greatsword and attack

2) Use the free interaction with object to sheathe his greatsword, draw the battleaxe and attack

3) Attack with his battleaxe and sheath it

4) Draw his pyke and attack

Quote from VoicesOfTheHighForest >>

The question is: in the third quote, does equipping or unequipping a weapon count toward that one free interaction with an object during your combat turn?

 No Equiping and Unequip a weapon as part of the Attack Action doesn't count toward your Time-Limited Object Interaction, nor is the drawing a Thrown weapon as pat of ranged attack.

The new SRD 5.2.1 has a conversion guide from SRD 5.1 to SRD 5.2.1 for creators looking to update their materials SRD v5.2.1 - System Reference Document - D&D Beyond 

It contains the following text confirming that you're intended to be able to equip and unequip on each attack of the Attack action;

Attack Action [Revised Rule] The Attack action contains several revisions:

• The action now specifies that it involves an attack with a weapon or an Unarmed Strike.

• The action now allows you to equip or unequip one weapon with each attack you make with the action.

• The ability to move between attacks during com bat is now a function of the Attack action rather than a general rule.