Fix NDI feed stagnation when capture pipeline is idle (#92)

[emosaru]

Summary

• Fixes NDI feed often stagnates and doesn't reach OBS with low ndi_frame_rate #92 — NDI feed stagnates during user inactivity, OBS declares the source dead.
• The hidden broadcast window's capture loop is driven by the main window's RequestAnimationFrame, which stops firing when the user is idle. With no fresh snapshots, the send thread had nothing to transmit and the NDI receiver timed out.
• Cache the last successfully sent frame and re-transmit it on the send thread's TryTake timeout (~250 ms) so the feed continues emitting frames whenever the capture pipeline goes silent. When state changes resume, fresh frames replace the cache and flow normally.

Implementation notes

• Extracted SendVideoFrame(...) helper from ProcessOneFrame so both the live and heartbeat paths share one code path.
• Cache stores the post-processed pixel buffer (un-premultiplied, drop-shadow composited, scaled) so the heartbeat resend doesn't redo work.
• Cached buffer released in Dispose.

Test plan

• Build with dotnet build (verified clean, 0 warnings)
• Run EmoTracker with EnableBackgroundNdi on, connect OBS as an NDI receiver, leave idle for 5+ minutes — feed should stay alive (previously went silent within ~1 minute)
• Make item changes — fresh frames still flow normally
• Close window — verify no exceptions during cleanup

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