feat: /api/system/health — one verdict for the whole stack (milestone 365 step 3)

The single endpoint the nav indicator and the System page will both read.
Composing a verdict is this module's job, not the UI's.

Two kinds of part, answered differently. LEARNED — celery roles and the GPU
agent, out of service_seen, where the question is "how long since it checked
in" and the answer can be "it has not". PROBED — Postgres and Redis, always
expected, never learned, because a last-seen for them would be actively
misleading: that Redis answered thirty seconds ago says nothing about now.

**The endpoint must never fail because something it checks has failed.** That
inversion is easy to write by accident and it destroys the feature exactly
when it is needed — a 500 when Redis is down instead of `redis: down`. Every
probe is wrapped, every wait carries a deadline (rule 156), and the roster
refresh swallows its own errors. The worst case is a part reported `unknown`,
which is a true statement about the system.

Postgres is probed first and gates the rest, because if it is unreachable
nothing else can be read — and "the database is down" is the most useful
single thing this can ever say.

The staleness thresholds are the design risk, not the code, and they are
deliberately generous: 90s to doubt, 300s to disbelieve. The constraint is a
deploy rather than a crash — `docker compose up -d` rolls start-first, so a
role is briefly served by two containers and then by neither while the old one
drains. Thresholds tight enough to catch a crash in seconds would paint the
page red on every update, and an alarm that cries wolf on every deploy is one
nobody reads. Tune down only after watching a real deploy pass through. The
numbers ship in the response so the UI can explain a `stale` without keeping a
second copy of them.

States are described in sentences rather than left as chips: "Scheduler has
not checked in for 6 min — treat it as stopped" is what someone needs at the
moment they are deciding whether to go and open Portainer.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01TTjbZZ6JirCMSaJzQV1RhA

backend/app/api/__init__.py

@@ -38,6 +38,7 @@ def all_blueprints() -> list[Blueprint]:
     from .suggestions import suggestions_bp
     from .system_activity import system_activity_bp
     from .system_backup import system_backup_bp
+    from .system_health import system_health_bp
     from .tags import tags_bp
     from .thumbnails import thumbnails_bp
     return [
@@ -51,6 +52,7 @@ def all_blueprints() -> list[Blueprint]:
         showcase_bp,
         settings_bp,
         system_activity_bp,
+        system_health_bp,
         system_backup_bp,
         admin_bp,
         cleanup_bp,