fix(health): AI dependency reads as failed during a container cold start

[Fluory]

Problem

GET /api/health reports "aiService": "failed" right after the AI container scaled to zero, although the service starts fine a few seconds later.

Evidence (2026-09-27)

First probe after the #73 deploy: aiService: failed; GET /healthz directly afterwards: 200 in 0.2 s, and the web health then ok. The web probe waits CHECK_TIMEOUT_MS = 3_000 (src/app/api/health/route.ts:10); the measured cold start of the container is about 5.6 s (ADR-0001 D11 amendment 2026-09-26).

Acceptance criteria

• A cold start does not read as an outage: either a probe timeout above the measured cold start for the AI dependency, or a distinct state (e.g. starting) – decided and justified in the PR
• The overall health status and HTTP code stay as they are for database and storage
• Runbook §8 names the behaviour

Security/Privacy affected?

No.

[Fluory]

Claimed by @Fluory on branch claude/fix-health-cold-start-81 (Freigabe des Orchestrators 2026-09-27: „mach das“).