This bug was fixed in Patch 1.77.146/1.45. Pets that are already missing from a save game need to be replaced manually.
I started a new save and now all families in Brindleton Bay are missing their pets. The households with Major Whiskers and Whitaker are empty.
Unclear but the issue only seems to affect new save games.
Pets and even strays seem to work as expected.
Only solutions is to replace the household with a version from either the gallery or the library. If you have an old save that still has them, you can just upload them to the library from there and then download into your new game.
If you don’t, you should be able to find a version in the gallery.