I’m pretty sure it’s a lot of quests, including some hidden ones. My wife and I both started new Exile’s Reach characters a couple of days ago. I had transferred a character and got hit with this; she had not.
She got the “100 quests” achievement on about the fourth quest, indicating all of the account wide quests she’d completed. I got the “50 quests” one much later, and I have been lucky enough to play a lot more than she has and I used to get the achievement earlier than her.
There’s a thread in bug reports where there’s a lot of information:
https://us.forums.blizzard.com/en/wow/t/pet-battlecollection-broken/681040