This is the first game I've played where pets don't roam in housing. It's sad really that ZOS hasn't implemented what's considered a basic housing feature in other games, so basic it's not even mentioned as one of the features. I even have a game from 16 years ago with pets that roam in housing, including modded pets inside modded housing.
It can't be that hard to implement. When pets (and mounts) are placed as items they are no longer pets but decorations. Give them their movement animations and make them roam like NPC AI do. I see cats and dogs roaming around everywhere in the game.
It's disappointing.