[RPG] Do the effects of a Potion of Speed or Potion of Heroism disappear if the character becomes unconscious

The neither of these things represents an if else block Here is the control flow:

• If you have surges left

  • Spend surge Regain HP, make saves

• Else If you are bloodied

  • Regain HP, make saves

• Else

  • No Effect

So in the case of either having surges or being bloodied you regain HP, if you neither have surges or are bloodied then the potion has no effect.

The key thing here is that the If Neither is referring to the condition of either having surges left OR being bloodied If one of these two things is true then you get to regain HP (spending a surge if you have one, not sweating it if you are out and bloodied), if neither is true then nothing happens.

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}