In a preview, the forge pill's panel says the pull's check: green, red with its first failing test, or running #6381

Later: The repository is FLOW ONLY until the #5930 alarms stay clear for 24 h, and this is preview-pill feature work.

Replaces #5827, parked twice (the check stayed red through two tries, then a run ended without a pull). Take it smaller when it comes back.

Done:

• [ ] A forge route answers, for a pull whose preview this is, { state: green|red|running, test?, log }, only to a viewer who may read that pull, and names its Server-Timing phases.
• [ ] The pill's panel on a preview shows check green, check red: <test> or check running, linking to the log. Production shows nothing new. The pill builds its DOM with no inline script and no style attribute.
• [ ] Tests cover the three states, a refusal for a pull the viewer cannot see, and the client source naming the three words.
• [ ] Run test/apps-door.test.ts alone before pushing: it checks the exact list of Server-Timing phases, so a new phase must be added there (this is what broke #6076).