Also happening to me. I am on PS5, no mods.
Edit: after playing around more, it seems to only happen with small dogs and puppies. I have not tested it on cats, but I imagine the same happens to kittens since you have to pick them up.
I can still adopt big dogs, adult or senior, but cannot adopt puppies. This goes for strays as well. I have no issue bathing my big dogs.
I also seem to have trouble interacting with puppies as a whole. If an interaction requires picking them up (eg feeling the love), the sim and puppy will just stay there frozen and it takes some time for the sim to put the puppy down and move again. (Or I click somewhere for my sim to move, cancel the puppy action, and eventually they start moving).
It also seems like just picking up the puppy, literally just the "pick up" action, does NOT freeze my sim or puppy and I am able to move around and place the puppy elsewhere.