The tunnel rejects everything waiting on its channel the moment one connect
attempt fails, even though it has already scheduled the next one with backoff.
That is right for app traffic, which retries for itself, but it made the
one-shot probe report a durable red "Unreachable" for a host that answers when
the user presses refresh a second later — a cold start is exactly when that
first attempt loses.
The probe now spans the tunnel's own reconnects within a 15s budget, and ends
immediately on a terminal tunnel state (auth failed, duplicate client, limit),
which waiting cannot resolve.