Diagnosing PgBouncer's max_client_conn limit
Covers PgBouncer's own client-facing connection ceiling — a different limit from Postgres's max_connections and from PgBouncer's server-side pool sizing. Does not cover prepared-statement errors under transaction pooling (see the two prepared-statement playbooks) or Postgres running out of connections directly (see the postgres-too-many-clients playbook).
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