It's not that unclear, is it? It says right in the PHB, "Drinking or administering a potion takes an action" (PHB, p. 144). That's under the Potion of Healing entry in the Equipment chapter.
Sure, and under Use an Object (PHB, p193) it says: "When an object requires your action for its use, you take the Use an Object action." Ergo, if you're drinking a potion you're taking the Use an Object action.
I'm not sure where "drinking a flask of water" comes from,
From common sense. The player says, "I want to drink the water in my flask." The DM thinks, "Ok, a flask of water is an object, and drinking it is using it. It doesn't seem like it would take more than 6 seconds to drink a cup or two of water. This is the Use an Object action."
unless you mean "drink all the ale in a flagon" in the Combat chapter. In which case I agree that "drink all the ale in a flagon" is a terrible example of what you can do in tandem with your movement and action. It can only be rationalized if you assume that the flagon is on hand, while the potion is in a backpack and has a stopper.
Perhaps I should clarify. I'm not talking about object interactions as a part of another action. I've never seen anybody try to do that.
What I have seen are people trying to drink potions as a bonus action when they're a Thief with Fast Hands, which explicitly allows the Use an Object action as a bonus action. Sage Advice ruled that they didn't intend you to use magic items with that ability including potions.
Rules as written though, it's 100% allowed just reading the PHB. I mean, the designers
clearly put Use an Object into the list of Combat actions. I assume they put it there for a purpose and to cover a certain set of actions, and they worded it so broadly that it pretty much has to cover magic items. They also explicitly put Use an Object onto the list of actions covered by Fast Hands. Clearly that's supposed to actually do something, too.
Honestly, I find it more interesting that nobody has players trying to use wands or other magic items as a bonus action. It's only been potions that this seems to come up.
It's only when you read the DMG that it's clear you can't do this:
Activating an Item said:
If an item requires an action to activate, that action isn't a function of the Use an Item action, so a feature such as the rogue's Fast Hands can't be used to activate the item.
Yeah, it actually calls out Fast Hands explicitly. Now, why they decided to bury this clause
in the flipping DMG and not put any reference to it in the Combat chapter of the PHB or the Rogue's Fast Hands ability is beyond me. It should at least say, "Magic items are not covered by the Use an Object action. If you're using a magic item, refer to the magic item rules in the DMG." I'm willing to bet that this was a complete oversight that they noticed after the PHB had gone to print.