For ATB the cooldown is visual and gates your turn, which gates your skills.
In the end this is all really just semantics, but again ATB (as implemented in most FF games) is best described as a turn cooldown, not a skill cooldown. In many of the games it is just a flexible, visual way to manage turn orders without relying on rounds -- where you simply rotate through each character. Some FF games freeze time once the ATB is full; others provide time freezing as an option (similar idea to previous Baldur's Gate games having real time + pause layered over a traditional round-based system).
Because ATB doesn't have rounds, it's possible for one character to have 2 turns (or any other arbirtrary number of turns) in the same amount of time another character has 1 turn. It's more realistic and provides a clearer advantage for fast characters, but it's more chaotic and can be harder to plan around. Either way, these are still "turns" in the tradional sense, and it's the turns that are experiencing a cooldown.
Anyway, not a system meant for BG3.

As if the fact that even the most minor conversation in this mess of a game cuts away to an unnecessary cinematic wasn't enough to kill the general pacing [...]
Oi! The cinematic camera during dialogue scenes is awesome. If you disagree with that then you're wrong. :P
Pathfinder: Kingmaker handles the rest system in an extraordinary way, actually assigning non-combat roles to people in order to turn resting into a light mini-game at the camp.
Solasta: Crown of the Magister doesn't go quite as in-depth, but at least there's still somewhat of a summary screen with some simple decisions to be made and the potential for ambushes.
Check out the example I provided earlier of Expeditions: Viking. Best camping minigame I've seen thus far.
Based on Early Access, I expect that Larian decided to ditch the "world map" of the original Baldur's Gate games. I don't believe that decision is really for the better. Regardless, if that's the way it's going to be, I think they should use rest points in a way a similar to Final Fantasy or Dark Souls. In this case, you would find a location that would be both camp site and fast travel point where you can long rest. You would put these in friendly villages, or before heading into a "dungeon", or at other points where it would make sense to take a break.
And then I would like it to have a camping minigame similar to Expeditions: Viking, with pretty cinematics like FFXV and conversations with your colleagues like in Dragon Age.