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I am also looking for it.
The only way to horizontally scale postgres is with replicas.
Supabase does some enhancements to that process in their backend from what I've seen documented but still uses the basic concept of read replicas. They also tie in PostgREST, not sure what would be involved with that on your own.
https://supabase.com/docs/guides/platform/read-replicas
There are guides out there for postgres scaling I'm sure.