[BGM-PR-15] Hardening, Concurrency Tests, and Docs

[slin1237]

Parent: #1214

Track: Hardening
Suggested milestone group: Hardening

Goal

Close the remaining operational and correctness gaps before shipping.

Acceptance Criteria

• Deterministic race tests exist for claim/claim, cancel/finalize, delete/finalize, and sweeper/worker interactions.
• End-to-end tests cover JSON create, streaming create, poll-to-terminal, cancel, delete, reconnect with starting_after, and include_obfuscation=false.
• Config and operational docs cover migrations, retention cleanup, timeout behavior, and backend support limits.
• The design doc and reference docs are updated to match shipped behavior exactly.

Dependencies

• [BGM-PR-08] GET, Cancel, and Delete Integration #1222
• [BGM-PR-10] Streaming Create and Live Tail #1224
• [BGM-PR-11] Conversation Linkage and Request-Context Replay #1225
• [BGM-PR-12] Postgres Wakeups, Startup Claim, and Claim Ticks #1226
• [BGM-PR-14] Oracle Polling Scheduler and Resume Tailing #1228

Out of Scope

• New background backends.
• Webhooks or cross-region coordination.