Print the app's address once both halves are up

Vite announces its own port on the way up, and that address does not
work: the server is the only origin, since it owns `/ws` and forwards
everything else. Following Vite's line gets a page that loads and a
socket that never opens — the app renders and then sits at "connecting",
which reads as broken rather than misaddressed.

The supervisor now probes the server until it answers and prints where
the app actually is. Probing rather than printing straight away puts the
line beneath Vite's banner instead of above it, and the server cannot
answer until Vite can — a 502 is it saying so — so a reply means both
halves are ready rather than merely started.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>