I think there are a lot of free hosts that could work?

  - Fly.io has a free tier that has postgres (if you want to debug from your workstation against live pg, which is useful, it's $2/mo for a public IP)
  - Supabase has a free tier (with the caveat that schema changes will resync the replica - which is fine as long as db is smallish)
  - AWS/RDS offers one year free

Those are just off the top of my head. Plus as jitl mentions you can just run the Dockerized pg in any free docker env.