[Epic 953][Stage II][chat-api][staging] Cut over Chat API staging API and worker to RDS

Parent epic: #953
Parent stage: #955
Component tracker: #961
Chat API staging tracker: #1021
Depends on: #1022, #1023

Goal

Switch Chat API staging API and task worker from CVM Postgres to the RDS staging target after CDC rehearsal and validation have passed.

Tasks

• Confirm encrypted-write readiness and CDC rehearsal acceptance criteria are complete.
• Drain CDC replication lag to zero or the documented cutover threshold.
• Pause or restart the Chat API worker deliberately during the final drain so worker writes do not race the final cutover point.
• Roll Chat API staging API and worker configuration to the RDS endpoint, RDS credentials, and required TLS settings.
• Keep the CVM-derived database field-encryption key configuration unchanged.
• Run Chat API staging smoke tests covering health, login/session flows, private-chat read/export behavior, account deletion, task worker resume behavior, and supported encrypted writes.
• Confirm old CVM Postgres receives no new Chat API staging writes after cutover.
• Define and observe the rollback window before retiring the old source.

Acceptance Criteria

• Chat API staging API and worker serve traffic from RDS successfully.
• Encrypted reads and encrypted writes work after the RDS cutover.
• Worker processing resumes cleanly without duplicate or lost task effects.
• Old CVM Postgres remains available as rollback source but is no longer written by Chat API staging.
• Monitoring shows acceptable latency, error rate, connection usage, locks, failed auth, and TLS behavior.
• Cutover notes are captured for the production runbook.

Start by reading the parent epic #953, stage tracker #955, component tracker #961, Chat API tracker #1021, and dependencies #1022 and #1023. Review their staging cutover and CDC validation details, then verify the listed API, worker, encryption, rollback, and monitoring acceptance criteria; done means the RDS cutover is validated and documented for the production runbook.