Supabase is an open source Firebase alternative. Start your project with a Postgres database, Authentication, instant APIs, Edge Functions, Realtime subscriptions, and Storage.

Supabase

Does anyone know why the PostgreSQL instance is exposed on 2 ports: 6543 and 5432 (the former is listed in Databas -> Connection Pooling -> Connection Info, the latter is listed in Settings -> Database -> Connection Info)?

https://redwoodjs.com/docs/connection-pooling

Other than connection pooling, do you know if PgBouncer enforce any other changes (e.g. changes to search_path, etc)?

Can read abt the pool modes:
https://supabase.com/blog/2021/04/02/supabase-pgbouncer

indeed, but this is still related to connection pooling - I am interested in whether PgBouncer makes any other changes to the session. For example, is PgBouncer responsible for the extra search paths for the public APIs (i.e. the setting in Settings -> API -> Extra Search Path)