[Feature]: Add extension audio export parity for click sounds

[crbender]

• I have searched the existing issues

Is your feature request related to a problem?

Yes. Today, click sounds from extensions are audible in preview, but they do not make it into exported MP4 audio. That creates a gap between what creators hear while editing and what viewers hear in the final video.

I reviewed related threads (#227, #443, #162), and the extension-first direction makes sense. I want to keep that direction and close the export parity gap.

Describe the solution you'd like

Add extension audio export parity so extension-triggered click sounds are captured and mixed into exported audio.

This should be implemented as a general extension audio path, not a one-off for a single extension.

Describe alternatives you've considered

1. Hardcode click sound in core editor: rejected, conflicts with extension-first direction.
2. Keep preview-only behavior: rejected, confusing for users and hurts trust in export output.

Additional context

• References: Mouse Click Sound & Subtitle Export #227, Feature: Auto-add synced click & typing sound effects to screen recordings #443, [Feature]: Cursor Enrichment & Setting Panel #162
• Goal: if an extension sound is intentionally triggered during export rendering, it should be present in exported audio with correct timing.

Acceptance criteria

1. Extension click sounds that trigger during export are audible in exported MP4.
2. No behavior change for users who do not use extension sounds.
3. Missing extension audio assets do not fail export; they are skipped with a clear warning.
4. Timing stays aligned with cursor interaction in the final output.

[crbender]

Adding implementation sequencing so this can be picked up in clean vertical slices:

1. [Feature]: Add extension host export audio capture lifecycle #573 extension host capture lifecycle
2. [Feature]: Ensure cursor:click event parity in export renderer #574 export cursor:click event parity
3. [Feature]: Add exporter model support for extension audio events #575 exporter model support for extension audio events
4. [Feature]: Mix extension audio events into offline/native export audio #576 audio mixing in offline/native export paths
5. [Feature]: Harden extension export audio path with safety guardrails #577 safety and resilience guardrails
6. [Feature]: Add regression and integration coverage for extension audio export parity #578 regression and integration coverage
7. [Feature]: Document extension audio preview/export behavior and author guidance #579 docs and release note updates

If this order looks good, I can open PRs one slice at a time so review and rollback stay straightforward.