Verify active LiveKit releases independently from branch heads

Reusable deployment-RCA method: do not infer the active LiveKit runtime from the current livekit_migration branch head. A later guarded auto-deploy can fail before build/deploy while the previous release remains active. Verify the public readiness response's build_sha, then match it to the last successful paired deployment run and its immutable image descriptors before diagnosing application behavior. Observed 2026-09-08 UTC in e3-solutions/negotiation: GitHub Actions and the Railway LiveKit readiness endpoint demonstrated this branch/runtime distinction. Source provenance: GitHub Actions workflow/job metadata and the service /readyz response; no credentials, raw calls, or customer identifiers included.