I want to be optimistic and say the fatigue mechanic either isn't properly implemented yet or simply is disabled for the first iteration of early access so Larian can get in-depth feedback about how the players handle individual encounters when they have access to all of their spells and abilities.

The pessimist inside me fears that exhaustion will be completely removed outside of spells like Sickening Radiance and that you'll be free to rest as much as you want to.
With Larian's talk about contemplating adding a loaded dice option for lower difficulties to help new players ease into the D&D mechanics, I imagine they'd also either remove exhaustion or heavily tone it down on lower difficulty levels.

Whatever might happen I just hope that the full release of the game won't make you feel like you're forced to rest because of arbitrarily defined metrics. Personally I like to attempt to go for as long as possible without resting since I like having to be mindful of health and spell slots (as opposed to just resting after every encounter) but in the current version of BG3 this means that I, apparently, miss out on a lot of companion dialogue since the companion quests only progress when you rest in a camp.