After a character has enough experience to level up, but before they have rested, should you calculate their experience as their current level or not yet new level.
(This is assuming a not RAW house rule of you need to have a rest first).
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According to the Player’s Handbook,
When a character earns enough XP, he or she attains a new character level ([…]).
Advancing a Level: When your character’s XP total reaches at least the minimum XP needed for a new character level ([…]), he or she “goes up a level.”
(Player’s Handbook, pg. 58)
If you have the XP, you have the level—no rest required. If you have the level, future challenges and rewards are calculated based on that level.
What you may be thinking of is the suggestions in the Dungeon Master’s Guide that “The rules in the Player’s Handbook assume that characters have access to everything they need to advance in level,” (pg. 197), and which then describe ways you can make learning skills and feats, spells, and other class benefits require in-character actions. However, each of these describes delays to getting some feature from your new level, not to gaining the level itself:
In your campaign, however, you can require that a character can’t learn a new skill or feat that he hasn’t been exposed to. […] One step further would be to require that a character have an instructor teach him new skills and feats. […] If you allow it, at the expense of a certain degree of realism, a character can obtain training ahead of time.
If you require wizards to actually spend game time on spell research to gain those new spells, assume it takes one day per spell […]
You can mandate that to gain any of the newfound class-based benefits earned by advancing a level, a character needs to perform some overall training. This training requires one week per every two levels, rounded up.
(Dungeon Master’s Guide pg. 197-198)
In every case, this training is envisioned as something you do after leveling up, but before you actually get one of the benefits that’s supposed to come with your level. The bit about skill and feat training even explicitly addresses the idea of training beforehand as an alternative option a DM might allow, “at the expense of a certain degree of realism.” (The claim that this is less realistic is, in my opinion, dubious if not outright wrong, but that’s what the book says.)
None of these suggestions mention rest, by the way.
So again, since you have the XP required, you have leveled up (even though you haven’t gotten any or all the features of that level yet), so that’s your level when calculating anything based on level, including further challenges and rewards.
If you haven't awarded the PCs their new level yet at all, you should award XP for their current level. If they're fighting using, for example, level 4 BAB, level 4 hp, level 4 spellcasting (at level 5, their full casters would get third level spells, a major gamechanger), then the challenges should still be compared to level 4, no matter what their XP total says.
(For what it's worth, I'm a fan of not handing out levels until the PCs sleep - it sidesteps a lot of weirdness and makes sense that they need some time to assimilate what they've learned. But you definitely shouldn't penalize them for your decision to wait, unless you simply want to incentivize them to make camp immediately when they get the XP for next level, regardless of what's going on...)