Exactly this. Whether it’s the Broken Shore entry scenario, or one of the pet battle dungeons, scenarios reset when you leave or go afk long enough to be logged out.
Also, while there is an introductory run where you can heal while in the dungeon, the real mode is completing the run without healing, and obviously, if you log out, you can heal on another character, so that’s a no-no.
You might like to do the earlier pet dungeons, Wailing Caverns and Deadmines, before you tackle Gnomeregan, by the way. You can pick up the quests for those in the pet shop in New Dala.
For cheat sheets for all the battles, Xu-Fu’s guides provides many strats:
https://wow-petguide.com/?m=Home
but it is much more satisfying to work your own way through.
Your collection does not include many of the most useful pets for battling. This list may point you to some that would hel you get through the dungeons more easily: