It doesn't. The rested bar grows longer. If it extends past the current level, it will be visible when you level up.
The exp you get from killing the enemies on the levequest does count. Just the reward at the end doesn't.
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I'm thinking the bar ticks up about 1 exp per 1 game minute tick... bar-wise anyway. I guess it's technically half that since only half that bar is actually extra exp. Either way, my original thought was it was 1 exp per second but after a night in the inn I found I had about half what I expected so 1 exp per game minute tick on the clock seems more accurate. I can't say I've noticed a cap but I know I've gotten a full bar as a 40 cul which was 70k+ tnl. I'd guess if there is a cap it's probably 50k bonus or 100k bonus, but I would half hope it wasn't that low.
Being offline for 18 hours extends my rested bar about 1/3 of the way whether I'm parked as level 39, level 32, or level 30. Seems like it hours away pretty fast. Need to keep eye on it about leves.
I've tested this. I just barely had the green bar on (I was very close to using up all the rested XP bonus) and I handed in a leve for 2500 xp.
The rested XP bonus MOVED along with the XP I just got. That is, I still had the bonus even after handing it the leve. Therefore, leve rewards do NOT consume your bonus.
was able to rest for about 5 days at lvl 37, bar went all the way to red, dinged 38 and still had a red bar, not the completion bonus for leves did not take away from my exp, unable to give a good estimation as i don't know how far the completion bonus pushed the bar further, but going with a low estimate i'd say eneough exp to go from just hitting 37 to half way to 39 before the bonus expired.
I'm going on holiday two weeks starting thursday and won't be able to access XIV so I will just remain in the Inn and see how much I've done when I return :D Two weeks should be more than enough to hit the cap.
Since Guardian's Aspect would regenerate at a rate of 20 per real life day (I think?), and the cap was 200, I'm gonna say that the rested XP cap is 10 days worth of resting.
Just my guess, based on the old system.
A better question - when is the first "tick" of rested XP accumulated? I'm guessing 1 hour in the room at minimum, perhaps half hour though. Alternatively, it could be connected to the in-game days.