skrog start right after wsl --shutdown times out (nightly e2e EmulationSurvivesAShutdown) #530

The nightly e2e fails intermittently: 3 of the 7 scheduled runs since 0.9.0 (2026-10-06, 10-08, 10-12), every time the same way:

--- FAIL: TestAcceptance/EmulationSurvivesAShutdown (132.4s)
    e2e_test.go:2496: skrog start after wsl --shutdown: exit status 1
        skrog: engine did not come up within 2m0s

Runs: https://github.com/wslkit/skrog/actions/runs/37455317762, https://github.com/wslkit/skrog/actions/runs/37769593362, https://github.com/wslkit/skrog/actions/runs/38246195820. There were no failures of this kind before #519 merged.

Cause

A race between skrog start and the outside-stop verdict from #518:

1. wsl --shutdown takes the engine's distro down. The supervisor has seen the engine running (sawUp).
2. skrog start writes desired=running and deletes the idle marker. Both are already in that state, so the supervisor's 250 ms file poke sees no change.
3. The next health tick (within 3 s) sees a down engine and a stopped distro, decides it was stopped from outside, and writes the idle marker.
4. Nothing wakes it. skrog start polls for 2 minutes and fails.

When the tick happens to land during wsl --shutdown itself, before skrog start runs, start's marker deletion is a real change and the engine comes back. That timing is why this fails on some runs and not others.

This is a product bug, not a test flake: any user who runs skrog start within a few seconds of wsl --shutdown hits it.

The supervisor.log that would have shown this directly isn't in the run's artifact; it's in the test's temp state dir, which gets cleaned up.