Well, in this case, nothing requires free object interaction because nothing explicitly says that. "Object interaction" isn't an action category, unlike Action or Bonus Action. Drawing a weapon isn't even a rule of itself, just an example: "you could draw your weapon as part of the same action you use to Attack".

There's a rule: "You can also interact with one object or feature of the Environment for free" and "If you want to interact with a second object, you need to use your action". Drawing an arrow does sound like "interacting with one object".

Taking two Attack Actions for whatever reason (Action Surge, Haste, etc) doesn't allow the character to draw two swords, so granularity between Attack Action and individual Attack doesn't really matter in this case.