fix(omo-senpi): bound the Kibitzer and facts shutdown awaits by the drain deadline (refs #8337)

senpi awaits session_shutdown handlers with no host cap, so the two pre-drain awaits
(Kibitzer sidecar shutdown, facts cancellation) could stall quit/reload/new/resume for as
long as a stuck sidecar mutex held them, and starved the drain steps that follow.

ShutdownDrain gains raceDetached(input, name, work): the work is always started - it is
what releases the wake lease and the sidecar directory owner lock - but it is raced against
the same deadline the drain steps share. On expiry the drain's existing budget warning is
logged with step: name, the handler returns, and the work continues detached with a late
failure warned instead of left unhandled.