🐛(frontend) hoist mute confirmation dialog to VideoConference level

`MuteButton` owned the confirmation dialog state locally. On the
participant tile, the button lives inside `FadeOverlay`, which
conditionally mounts its children based on tile mouse activity
(3 s idle timeout). Once the user moved the pointer onto the
react-aria portal, mouse events on the tile stopped, the idle timer
expired, `FadeOverlay` unmounted `MuteButton`, and the dialog was
destroyed with it — hence the "closes randomly" behavior.

Render the dialog once at the VideoConference level via a shared
`MuteAlertDialogProvider`, so its lifetime is independent from any
button that opens it.

CHANGELOG.md

@@ -29,6 +29,7 @@ and this project adheres to
 - 🐛(frontend) treat client-initiated connect aborts as events
 - 🐛(frontend) use state instead of a ref for MoreControls container
 - 🐛(frontend) stop init_virtual_background from firing on blur updates
+- 🐛(frontend) hoist mute confirmation dialog to VideoConference level
 
 ## [1.27.0] - 2026-08-14