This is a good time to be offering hybrid search extensions. I just did that myself recently with pgvector for a documentation site.
Does ParadeDB work with Render? They seem to have a whitelist of extensions https://render.com/docs/postgresql-extensions
We just made a blueprint for it! https://github.com/paradedb/render-blueprint
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 :)