- Uses shared SectionShell/DropdownItem from ./_shared/SettingsPickerPrimitives
rather than redefining local copies (parity with AudioInputSection).
- supportsSinkId is reactive to AudioContext lifecycle via the audioCtxGen
pattern (bumped by AudioManager.onResumed). Defaults to true and only flips
to false when a real context exists AND lacks setSinkId (Safari < 17), so
the picker is never preemptively hidden when the user opens Settings before
joining voice. AudioManager.setOutputDevice + initContext re-apply path
handles the deferred sinkId binding once the context appears.