Step 1 · StartPgBouncer is refusing new client connections
This is PgBouncer's own max_client_conn — the number of frontend (application-side) connections it will accept — not Postgres's max_connections, and not PgBouncer's server-side pool size (default_pool_size / max_db_connections). Those are three independent limits.
What happens next
- passed → step 2, Check current clients against the configured limit