[RPG] Can an unconscious person drink a potion

No.

Drinking a potion is explicitly an action.

Healing Potion:.... Drinking or administering a potion takes an action (PHB 153)

You can draw the potion as a part of the action that you use to drink it, but you cannot drink it as a free action.

However, it takes an action and cannot be used with the Rogue's Fast Hands ability per the DMG(p141):

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 rogue's Fast Hands can't be used to activate the item.

Thus you don't have 2 instances of interact with object going on, you have 1 interact with object (drawing the potion), and a second action that is specific to the magic item in question. This is quite different from two instances of interact with object.

Drinking/administering a potion takes an action, as you cited from DMG at p.139. That's the general rule in effect, unless specifically contradicted.

You note that the DMG's description of the Potion of Healing doesn't mention that it requires an action to consume, and seem to be wondering if that omission is meant to signal something. But every other potion described in the DMG also omits any description of the mechanics of drinking potions: they just start with phrases like "when you drink..." or "for one hour after drinking...." So we can't read anything into the omission, or the general rule would apply in no cases. (DMG5e pp.187-8)

So why does the PHB call out the consume action in its Potion of Healing description?

The Potion of Healing is the only potion described in the PHB (p. 153); the PHB doesn't have a general "potions" section akin to the DMG's on p.139. So this is the natural place in the PHB to mention that interaction with the action economy¹. Would it have been clearer to add to the sidebar on p.190? Maybe, but that's a sidebar full of free interactions, not examples of things that aren't-free-interactions-though-you-might-think-they're-just-the-same.

Sidebar: But I can quaff an entire flagon...

Yeah, this bugged my table too. We made in-world sense of it by saying that a magical potion is an... unusual enough mouth-experience to take a moment² to consume. A flagon of ale... apparently the game designers assume our characters are more-inured to that experience than to the experience of drinking spells.

^{1 - it's also mentioned in the Herbalism Kit, but that's the least-natural place to talk about the potion's consumption.}

^{2 - I think about trying to get my kids to take emoxicillin and Wish it only took six seconds =P}