By RAW, can you use your free object interaction while taking the "Use an Object" action?

Question

There is a drinking contest between a Dwarf and a Halfling to see who can drink flagons of ale the fastest. Normally one would assume the Dwarf would have an advantage at drinking, but unbeknown to them the Halfling is a Thief.

From the rules for Interacting With Objects Around You

Here are a few examples of the sorts of thing you can do in tandem with your movement and action:

• drink all the ale in a flagon

From the rules for the Use an Object action:

You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. When an object requires your action for its use, you take the Use an Object action. This action is also useful when you want to interact with more than one object on your turn.

Can someone taking the Use an Object action to drink 2 flagons of ale in a single action?

Can a Thief take Use an Object, then use Fast Hands to Use an Object again, then move 0ft, drinking 5 flagons of ale in a single turn?

In the quote above I have italicised a sentence, does this limit you to 1 object interaction per turn for free, or is this an explanation why someone would ever use this when they can interact with objects for free?

Note: I know that using action surge you could drink even more flagons of ale in a turn, this isn't an optimisation question, the ale drinking is just an example. If you want to present a more powerful drinking champion then go ahead, after the question is answered :)

Also note: I am interested in the official rules. This means a RAW reading to the best of your ability

If you want to provide some houserules about interacting with objects, please do so after first addressing RAW/RAI so as not to create partial answers.

Answer 1

The Rogue could drink 3 flagons

The section on "Other Activity On Your Turn" states:

You can also interact with one object or feature of the environment for free, during either your move or your action.

It later presents a list of things you can do "in tandem with your movement and action". This limits your number of free object interactions to one per turn and does not limit during which action you can take an object interaction.

Thus the Rogue could spend an action to Use An Object (drink a flagon), drink a flagon as an object interaction at that time, and then use Fast Hands to take the Use An Object action again, drinking their third and final flagon.

---

Sidenote: The Fighter's Action Surge feature would allow them to drink one additional flagon by taking the Use An Object action; similarly the haste spell would allow you to drink one additional flagon by taking the Use An Object action.