(ParadeDB maintainer here). This is super cool. Congrats on the project, and I'm excited to see ParadeDB be used to power this kind of use case. If there's anything else you need to ship Omni, don't hesitate to reach out to me!
Does ParadeDB work with Render? They seem to have a whitelist of extensions https://render.com/docs/postgresql-extensions
One-click deploy with Render, and we're directly in contact with the core team to get it added to their official docs. I hear the PR is up internally :)