PgBouncer maintainer here, so obviously biased. But I think currently PgBouncer should still be the default connection pooler that you choose. There's a few newer options: Odyssey, pgcat, and supavisor. But all focus on a solving 1 or 2 specific problems that PgBouncer did not solve well, while not solving many of the other problems that PgBouncer does solve. So if you have the exact same requirements as the authors of those tools, then switching might be good. But otherwise you should probably continue using PgBouncer.

Supavisor specifically is too immature for general usage IMHO. It's missing some really core functionality like query cancellations: https://github.com/supabase/supavisor/issues/174 Also it's now the only connection pooler without prepared statement support.

I did a talk on this exact topic at PGConf NYC recently. My slides are here: https://github.com/JelteF/slides/raw/main/2023-10-05-future-...