Connects, and PROVES the root is writable rather than assuming it.

The probe exists because of X8-9: a scaffolded Deno project's start task requests --allow-net --allow-env --allow-read --allow-sys and no --allow-write, so every upload failed while /health reported up — the M70c liveness probe calls stat, a READ, which the granted --allow-read satisfies. Three defects had to be understood before the one-flag cause was visible. Failing here instead, with the flag named, follows this repo's rule of failing at registration with a name rather than at the first request with a bare error.

A startup probe rather than a per-check write: writability changes almost never, and a write on every health-probe interval is recurring I/O for a fact that does not move.