Desktop: Add option to mute Floating Bar in-app notification previews (respect Focus/DND)

[omi-discord-vector]

Problem

On macOS Desktop, assistant notifications are shown twice:

1. as a Floating Bar in-app preview below the bar, and
2. as a native macOS notification.

The in-app Floating Bar preview is not affected by macOS Focus/DND, so users can't quickly silence it using system controls.

This also makes the Floating Bar appear to "randomly re-enable" itself when notifications arrive (it is shown temporarily to render the preview).

Requested

Add a setting to control Floating Bar notification previews independently from native macOS notifications, e.g.

• Toggle: Show notification previews in Floating Bar (on/off)
• Optional: Respect Focus/DND (auto-mute in-bar previews when Focus is enabled)
• Optional: Only show in-bar previews when Floating Bar is enabled

Expected behavior

Users should be able to keep native notifications (which respect Focus/DND and offer OS-level customization) while silencing Floating Bar previews without having to disable all notifications in-app each time.

Notes

Implementation hint: NotificationService.sendNotification(...) currently calls FloatingControlBarManager.shared.showNotification(...) before sending the native notification.

Reported by: Discord user (alicja.szeptem) in #desktop-app