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
The material is covered in the Adventurers' League Player's Guide. It changes each season, so it is best obtained from the Dungeon Master's Guild as part of the Player's Pack. It's a free download, though you do need to register for the site.
Adventurers' League primarily functions on the honor system. There is no master record that needs to be updated anywhere, just the two character's log sheets.
Basic Requirements
- Only permanent magic items can be traded; consumables like potions and scrolls cannot be traded (they can be shared while at the same table, but if unused, possession reverts to the owner at the end of the session).
- The items to be traded must have matching rarities. If you want a Rare item, you have to have a Rare item to swap for it. Items without a rarity are considered "unique," and may not be traded.
- Certificates are no longer required, unless the item does not have a published rarity. If the rarity is only established/printed on the certificate, then the certificate must go with the trade. If the player does have a certificate, and it is not required to establish rarity, it must be destroyed or physically handed off.
Same Table
Players simply swap the magic items and note the change - include the character name, player name, and player's DCI number (if available) and you're all set.
I like to record which adventure or module the player got the item from. They should have all this information on their own adventure log. If they don't, you should be wondering how they got the item to begin with. Plus, some items have special minor functions that are unique to the source - for example, the Bracers of Archery from one particular module also provide protection against high and low temperatures. Bracers of Archery obtained by other means lack this extra benefit.
Different Table
Each player deducts 15 downtime from their character and proceed as above. The downtime reflects the characters meeting each other somewhere or working with third-party agents to facilitate the trade.
Self Trades
If the same player controls both characters, they can never meet at the same table. Conduct the trade like a different table trade - both characters pay the downtime.
On Seasons
This answer was originally written during Season 7. Season 8 added an additional requirement of matching the Magic Item Table from the DMG. As of Season 9, the magic item trading rules have gone back to how they were in Season 7 (minus lifestyle expenses, which I removed the reference to anyway). Who knows what will happen when Season 10 rolls around sometime in late 2020 or early 2021.
Best Answer
Potions are magic items.
From the Dungeon Master’s Guide:
Potion of healing (all rarities) is found in the magic items chapter of the Dungeon Master’s Guide, and potions are explicitly described as magic items.
We also find a common potion of healing described in the equipment section of the Player's Handbook:
A potion of healing is a magical red fluid.
Additionally, in Eberron: Rising from the Last War, there is a section called “Creating Common Magic Items”, which says:
In this section, potion of healing appears in a table column labeled “common magic item”.
Does the phrase "a character must have proficiency in the tools used to create a nonmagical version of the item" imply that you can create mundane potions of healing with an herbalism kit?
No. Rules for creating potions of healing with an herbalism kit of found in Xanathar's Guide to Everything, here we see:
Even when created with an herbalism kit, they still count as magical items.
The DDB character sheet is not official rules material.
Every once in a while DDB’s implementation of the rules into the character sheet tool leads to confusion as some things are misrepresented. Here is an example. The rules are quite clear that potions of healing, even common ones, are magical, and anything in the character sheet implying otherwise is an artifact of the character sheet.