feat(gateway,storage): mosaic gateway doctor with tier health JSON (FED-M1-06)

Adds `mosaic gateway doctor [--json] [--config <path>]` for tier-aware
health reporting (postgres, valkey, pgvector). JSON mode emits a single
parseable TierHealthReport for CI consumption; exit 1 on red.

Refactors gateway-internal tier probes into @mosaicstack/storage so the
same probe logic is reused by both the gateway boot path
(detectAndAssertTier — fail-fast on first failure) and the doctor
command (probeServiceHealth — non-throwing, runs all probes, returns
report). Old apps/gateway/src/bootstrap/tier-detector.* files removed.

A local TierConfig interface in tier-detection.ts captures the minimal
structural shape from MosaicConfig without importing @mosaicstack/config
(would create a cycle since config already depends on storage for
StorageConfig).

Tests:
- packages/storage/src/tier-detection.spec.ts — 22 tests (11 ported from
  gateway tier-detector, 11 new for probeServiceHealth + timing + branch
  coverage)
- packages/mosaic/src/commands/gateway-doctor.spec.ts — 12 tests for
  JSON contract, exit codes, output format, --config override

Refs #460

docs/federation/TASKS.md

@@ -21,8 +21,8 @@ Goal: Gateway runs in `federated` tier with containerized PG+pgvector+Valkey. No
 | FED-M1-02 | done        | Author `docker-compose.federated.yml` as an overlay profile: Postgres 17 + pgvector extension (port 5433), Valkey (6380), named volumes, healthchecks. Compose-up should boot cleanly on a clean machine.          | #460  | sonnet | feat/federation-m1-compose      | FED-M1-01  | 5K       | Shipped in PR #471. Overlay defines `postgres-federated`/`valkey-federated`, profile-gated, with pg-init for pgvector extension.   |
 | FED-M1-03 | done        | Add pgvector support to `packages/storage/src/adapters/postgres.ts`: create extension on init (idempotent), expose vector column type in schema helpers. No adapter changes for non-federated tiers.               | #460  | sonnet | feat/federation-m1-pgvector     | FED-M1-02  | 8K       | Shipped in PR #472. `enableVector` flag on postgres StorageConfig; idempotent CREATE EXTENSION before migrations.                  |
 | FED-M1-04 | done        | Implement `apps/gateway/src/bootstrap/tier-detector.ts`: reads config, asserts PG/Valkey/pgvector reachable for `federated`, fail-fast with actionable error message on failure. Unit tests for each failure mode. | #460  | sonnet | feat/federation-m1-detector     | FED-M1-03  | 8K       | Shipped in PR #473. 12 tests; 5s timeouts on probes; pgvector library/permission discrimination; rejects non-bullmq for federated. |
-| FED-M1-05 | in-progress | Write `scripts/migrate-to-federated.ts`: one-way migration from `local` (PGlite) / `standalone` (PG without pgvector) → `federated`. Dumps, transforms, loads; dry-run + confirm UX. Idempotent on re-run.         | #460  | sonnet | feat/federation-m1-migrate      | FED-M1-04  | 10K      | Do NOT run automatically. CLI subcommand `mosaic migrate tier --to federated --dry-run`. Safety rails.                             |
-| FED-M1-06 | not-started | Update `mosaic doctor`: report current tier, required services, actual health per service, pgvector presence, overall green/yellow/red. Machine-readable JSON output flag for CI use.                              | #460  | sonnet | feat/federation-m1-doctor       | FED-M1-04  | 6K       | Existing doctor output evolves; add `--json` flag. Green/yellow/red + remediation suggestions per issue.                           |
+| FED-M1-05 | done        | Write `scripts/migrate-to-federated.ts`: one-way migration from `local` (PGlite) / `standalone` (PG without pgvector) → `federated`. Dumps, transforms, loads; dry-run + confirm UX. Idempotent on re-run.         | #460  | sonnet | feat/federation-m1-migrate      | FED-M1-04  | 10K      | Shipped in PR #474. `mosaic storage migrate-tier`; DrizzleMigrationSource (corrects P0 found in review); 32 tests; idempotent.     |
+| FED-M1-06 | in-progress | Update `mosaic doctor`: report current tier, required services, actual health per service, pgvector presence, overall green/yellow/red. Machine-readable JSON output flag for CI use.                              | #460  | sonnet | feat/federation-m1-doctor       | FED-M1-04  | 6K       | Existing doctor output evolves; add `--json` flag. Green/yellow/red + remediation suggestions per issue.                           |
 | FED-M1-07 | not-started | Integration test: gateway boots in `federated` tier with docker-compose `federated` profile; refuses to boot when PG unreachable (asserts fail-fast); pgvector extension query succeeds.                           | #460  | sonnet | feat/federation-m1-integration  | FED-M1-04  | 8K       | Vitest + docker-compose test profile. One test file per assertion; real services, no mocks.                                        |
 | FED-M1-08 | not-started | Integration test for migration script: seed a local PGlite with representative data (tasks, notes, users, teams), run migration, assert row counts + key samples equal on federated PG.                            | #460  | sonnet | feat/federation-m1-migrate-test | FED-M1-05  | 6K       | Runs against docker-compose federated profile; uses temp PGlite file; deterministic seed.                                          |
 | FED-M1-09 | not-started | Standalone regression: full agent-session E2E on existing `standalone` tier with a gateway built from this branch. Must pass without referencing any federation module.                                            | #460  | haiku  | feat/federation-m1-regression   | FED-M1-07  | 4K       | Reuse existing e2e harness; just re-point at the federation branch build. Canary that we didn't break it.                          |