Temporarily mute system playback during voice capture

### Describe the feature or problem you'd like to solve

Temporarily mute system playback while voice capture is active. For example, I may be listening to Spotify when I press the keyboard shortcut to speak to Copilot. The speaker audio can interfere with microphone capture, so I would like playback muted immediately and restored when I finish talking.

### Proposed solution

Add an option such as **Mute system playback while listening**. When voice capture begins, Copilot should save the current output device and mute state, then mute the active playback device. When capture ends or is cancelled, it should restore the saved state rather than simply toggling mute.

This would improve transcription quality and prevent background audio from being captured without requiring users to manually pause or mute other applications.

### Example prompts or workflows

- While Spotify is playing, press the Copilot voice shortcut; playback is muted until voice capture ends.
- Cancel voice capture; playback immediately returns to its previous state.
- Start voice capture while the output is already muted; it remains muted afterward.
- Switch output devices, including a Bluetooth profile change, while capturing; Copilot safely restores the device state when capture ends.

### Additional context

This appears feasible on all three desktop platforms without elevated privileges:

| Platform | Feasibility | Native mechanism |
| --- | --- | --- |
| Windows | High | Core Audio [`IAudioEndpointVolume`](https://learn.microsoft.com/windows/win32/api/endpointvolume/nn-endpointvolume-iaudioendpointvolume) exposes `GetMute`/`SetMute` for the default render endpoint. |
| macOS | High | Core Audio exposes [`kAudioDevicePropertyMute`](https://developer.apple.com/documentation/coreaudio/kaudiodevicepropertymute), readable and writable through AudioObject property APIs on supported output devices. |
| Linux | Medium-high | PipeWire/WirePlumber supports muting the default sink (for example, [`wpctl set-mute @DEFAULT_AUDIO_SINK@`](https://pipewire.pages.freedesktop.org/wireplumber/tools/wpctl.html)); PulseAudio exposes [`pa_context_set_sink_mute_by_name`](https://freedesktop.org/software/pulseaudio/doxygen/introspect_8h.html). The implementation needs backend/runtime detection across distributions. |

Cross-platform implementation considerations:

- Snapshot the output device identity and prior mute state before changing it; do not implement this as a blind toggle.
- Restore state on every normal completion, cancellation, and error path. Because endpoint mute can survive a process crash, persist enough temporary state for best-effort recovery on the next launch.
- Handle default-device changes during capture, especially Bluetooth devices switching between high-quality playback and headset profiles when the microphone opens.
- Check whether the selected device actually exposes a writable mute control. If not, report that the option is unavailable rather than silently changing volume.
- Avoid overwriting a mute-state change the user makes manually while voice capture is active.

Muting all system playback would be simpler and more predictable than targeting individual applications such as Spotify. Per-application muting could be considered separately but varies more significantly by platform and audio backend.

Aucun fichier, test ou point d’entrée n’est nommé. Commencez par localiser les chemins existants de démarrage, d’achèvement, d’annulation et d’erreur de la capture vocale, puis identifiez les intégrations audio de la plateforme. Le travail est terminé lorsqu’une fonctionnalité de mise en sourdine facultative capture l’appareil de sortie et l’état de mise en sourdine, les restaure de manière sûre sur tous les chemins de sortie et gère les changements d’appareil ainsi que les contrôles de mise en sourdine indisponibles.

Rédigé par le modèle d'indexation à partir du texte de l'issue.