run: implement the adapter-owned unified seat health probe

[solomonneas]

Parent: #474
Design: PR #575 and docs/proposals/2026-07-26-seat-health-probe-and-worker-failure-taxonomy.md

Build the shared probe coordinator and adapter check matrix. This issue writes health receipts and feeds roster doctor, but does not enforce run routing.

Acceptance criteria

• Probe declaration, executable identity, auth and entitlement, transport liveness, version gates, exact model reachability, and isolation compatibility when applicable.
• Cover direct, endpoint, Codex exec, Codex app-server, and Cursor ACPX seats through adapter-owned checks.
• Probe requested seats and declared fallback chains in parallel with 30-second per-seat and 35-second overall deadlines; model reachability receives at most 15 seconds.
• Use the proposal fingerprint and five-minute healthy and 30-second unhealthy cache rules.
• Write atomic brigade.seat_health.v1 receipts with bounded details, variable names without values, and redacted endpoint data.
• Run model smoke checks only in a temporary Git repository.
• Make roster doctor render the shared result while retaining current public labels.
• Fixture adapters verify healthy, degraded, auth, version, model, transport, hang, timeout, and redaction behavior without live credentials.
• ./scripts/verify passes through brigade work verify run.

Dependencies

Blocked by #576. This is implementation step 2.