Playing 1.18.11 (on mac, for mc version 1.20.1), and I noticed that, upon unlocking Pack Puppy, I don't see the button for my dog's inventory in my inventory--but only in survival mode. It's there in creative mode (and I can access it in the dog menu as well), but specifically in the survival mode inventory it's just not there.

Player inventory--the pack puppy one works just fine, oddly enough.

Are you refering to the dog inventory button in your player inventory or the one located in the Dog GUI > Train > Pack Puppy?

I'm having this same issue (quilt/fabric 1.20.1) - at first, i wondered if it was because Trinkets was covering it up and went to look for a config file to move the gui button and noticed that isnt configurable. Any chance it could be in future?
Additionally/alternatively, a bindable hotkey for opening Pack Puppy inventories could circumvent button rendering issues entirely!