I've never heard of such a thing, and a quick Google search didn't find anything -- is this a real movement, or something you heard from someone you know?
The closest I could find was a movement to support the right to have pets in apartments and/or public housing.
It isn't a real thing in that I haven't heard of any actual politicians advocating for it in the US. However, I just learned that mandatory pet
This [1] and this [2[, were top non-sponsored results when I google searched "manditory pet insurance".
I also noticed that Spain has introduced mandatory registration, liability insurance, and training classes for all dog owners in the country.
https://dogstodaymagazine.co.uk/2023/02/15/great-debate-shou...
https://www.reddit.com/r/changemyview/comments/iohxzf/cmv_pe...