On a Realm survival world, I am unable to level villagers past level 2.
I had four level 1 villagers (3 shepherds, 1 librarian) that had been traded with but were still level 1 prior to updating to 1.16.0. I was able to successfully level them to level 2 but when I tried to level them to level 3, after their XP bar was filled, it emptied without a level increase and with no new unlocked trades.
I also had a level 2 librarian that I tried to level to level 3 that exhibited the same behavior. I have attached screenshots. You can see the trade processed (+1 lantern, -1 emerald) but the villager XP was reset and excess XP applied but level remains at 2 and no level 3 trades are unlocked.
Unfortunately, I was not able to replicate this using creative mode so I am not certain what conditions are needed to cause this issue.