fix(engine): preserve streaming encoder termination diagnostics

[jrusso1020]

What

Preserve the streaming encoder's termination reason and frame counts in both getExitError() (used by capture-loop early failures) and close(). Watchdog termination remains a failure even if the child exits with code zero.

Why

Addresses the remaining observability gap in #3744. On current main, ManagedChildProcess knows whether it requested termination for inactivity or cancellation, but getExitError() discards that reason. close() only includes the timeout context on its nonzero-exit path. Neither error records how many frames were attempted or accepted.

The reported v0.6.52 also had an older backpressure bug: it reset the watchdog only when stdin.write() returned true, never after a buffered write drained, and capture callers ignored the return value. #1372 already added drain waiting, heartbeat refresh after drain, and capture-loop stop guards. That is a plausible mechanism for the old report, but the original composition is unavailable and the actual SIGTERM sender cannot be established from the supplied logs.

How

Snapshot attempted/accepted frame counts and pending-drain state immediately before a managed termination request, or at process settlement for other exits. Accepted counts writes queued by Node, including writes returning false; it does not claim FFmpeg encoded those frames. Late write attempts cannot overwrite the snapshot. Both error surfaces share the formatter and preserve external-interruption retry classification.

For slow software capture, use a current release with #1372 first. A progressing render can exceed the total inactivity budget. If disk-backed capture is needed, PRODUCER_ENABLE_STREAMING_ENCODE=false selects that path; PRODUCER_ENABLE_CHUNKED_ENCODE=true alone does not disable streaming. This change leaves those defaults unchanged.

Test plan

• Unit tests added/updated: four regression assertions fail against unmodified main; all pass with this change.
• 76 engine tests pass: streamingEncoder, managedChildProcess, runFfmpeg.
• Four producer ensureFrameWritten tests pass.
• Engine TypeScript check, changed-file oxlint/oxfmt, and diff whitespace check pass.
• Manual testing performed: original production composition was not supplied; no claim of reproducing its DOM-heavy render.
• Documentation update not applicable: diagnostics use the existing error API.