After a planned database failover (promoting a standby to primary), several application instances continue trying to write to the old primary for several minutes.

This usually indicates the application is caching the database connection/hostname resolution rather than re-resolving it, or the failover mechanism didn't update DNS/service discovery promptly enough for clients to pick up the change. Diagnose connection pool and DNS TTL/caching behavior in the application's database driver configuration, and ensure the failover process actively triggers reconnection (or that connection pools have a reasonably short max-lifetime forcing periodic reconnection) rather than assuming clients will detect the change passively.