The human-pause delays leave start() in-flight for several seconds, which
exposed two races:
- stop() during a pause only ended the pause; start() continued and called
joinVoice on the streamer stop() had already nulled (null deref).
- `active` was set only just before go-live, so a second /stream during the
delay passed the guard and both calls raced on the same overwritten streamer.
Now start() locks `active` before any await, keeps controller/streamer/capture
as local refs, and calls signal.throwIfAborted() after each await so an
interleaved stop() unwinds into a catch that tears down via the local refs and
clears instance state only if it still points at this attempt. isActive() now
reflects "starting" during the delay too.
Verified live: concurrent start is rejected ("이미 송출 중입니다"), stop() mid-
startup returns a cancel message with isActive=false and no uncaught error, and
the happy path still goes live and tears down cleanly. tsc --noEmit passes.
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