The ProviderHealth layer blocked server startup with two sequential CLI
spawns (codex --version + codex login status), each with a 4-second
timeout, delaying startup by up to 8 seconds.

Run health checks in the background via Effect.runPromise so the layer
resolves immediately with a placeholder status. Add an onReady callback
to ProviderHealthShape so wsServer can push the resolved statuses to
connected clients once checks complete, preventing early-connecting
clients from showing "Checking..." indefinitely.