diag: log what the broadcast is actually bound to while a stream runs

The logs answered the question and closed off a whole branch of investigation.

The long run: broadcast inserted 14:17:04.577, ffmpeg to
rtmp://a.rtmp.youtube.com/live2/5f6z-... at 14:17:05.686, and ffmpeg's own
muxing summary at 14:18:56.473 reads

  video:101229KiB audio:1419KiB  muxing overhead: 0.202949%

~99MB of real video plus audio over 112s, which is what 8000+128 kb/s is
supposed to produce. No socket error, no 4xx from ingest, no reconnect. And the
broadcast still never left `ready`; close-out 403'd invalidTransition again. The
8s run behaved the same way, so "YouTube needed longer" is disproven — 112s is
longer.

So the RTMP path is provably healthy. That is the finding worth keeping: it
kills the entire "the push is broken" theory, which is where this had been
heading for a week. The break is between ingest being accepted and the broadcast
being told to start.

Which puts the binding in frame, and the app was structurally blind to it.
Google documents contentDetails.boundStreamId and says enableAutoStart fires
"when you start streaming video on the bound live stream" — both valid on
insert, neither restricted against reusable streams. But the migration guide
also says a broadcast "is not bound to any streams at the time that it's
created", and the failure that produces is invisible from the RTMP side
precisely because a reusable stream will happily accept bytes for an unbound
broadcast. Ingest succeeding proves nothing.

Hence LogBroadcastDiagnosticsAsync, riding the existing health poll rather than
adding a timer. One greppable line: lifecycle status, privacy, recording,
boundStreamId *compared against the stream id we are actually pushing*
(BoundMatches: yes / MISMATCH / NO-BINDING / unknown), boundStreamLastUpdate-
TimeMs, autoStart/Stop, liveChatId presence, the stream's own streamStatus and
activeLiveChatId, and the CDN settings we declared.

Deliberately self-limiting: _broadcastSeenLive latches on live/liveStarting so
the diagnostic shouts only while the broadcast is stuck and goes quiet once it
is healthy. A permanent per-tick log line would be noise; this is the opposite.

One test, per the Good Dog rule: BroadcastBindingTests pins the matrix and
specifically pins `unknown` when there is no stream id to compare against, so a
missing expectation can never be misreported as a match — that is the failure
that would make this diagnostic lie.

Suite 387/387, 0 warnings.

ViewModels/MainViewModel.Streaming.cs

@@ -21,6 +21,9 @@ public partial class MainViewModel : ViewModelBase
     private string _streamDescription = string.Empty;
     private string _streamVisibility = "Private";
     private string? _currentBroadcastId;
+    /// <summary>Latches once the broadcast reaches live so the per-poll broadcast
+    /// diagnostic stops logging (2026-10-04). Reset at broadcast creation.</summary>
+    private bool _broadcastSeenLive;
     private string? _reusableStreamUrl;
     private ReusableStream? _reusableStream;
     private string? _healthIssueBanner;