feat(ui): render the Context mode switch from a store

ContextControls presents the selected mode, the transition busy state and the nearby sites search through a publish option, and ContextView renders them from the gev-context store. ./ui/context stays free of Vue. The Radio QA reads the search button's aria-busy, the state it actually carries.

docs/VUE-MIGRATION.md

@@ -108,7 +108,10 @@ They contain no application state.
    card that LocalSdrControls publishes beside it; fields a person edits take
    their value through `v-field-value`, which never writes a focused field;
    the tuner and the Cockpit radio controls keep their owners' element
-   bindings), the command dock,
+   bindings; `ContextView` renders the mode switch and the nearby sites
+   search from the `gev-context` store, which ContextControls reaches only
+   through its `publish` option, so `./ui/context` needs no Vue), the
+   command dock,
    the phone shell, then Cockpit. Layers that write into the right rail
    directly gain a slot instead.