feat: persist listen mode across views via localStorage

Extract listen mode into a shared useListenMode() composable backed by
localStorage ('fa_listen_mode'). ChatView and BriefingView both use it,
so toggling auto-read on in one view keeps it on after navigation or
page refresh — no need to re-enable it each visit.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/composables/useListenMode.ts

@@ -0,0 +1,14 @@
+import { ref, watch } from 'vue'
+
+const LISTEN_MODE_KEY = 'fa_listen_mode'
+
+// Shared across all views — persisted to localStorage
+const _listenMode = ref<boolean>(localStorage.getItem(LISTEN_MODE_KEY) === 'true')
+
+watch(_listenMode, (v) => {
+  localStorage.setItem(LISTEN_MODE_KEY, String(v))
+})
+
+export function useListenMode() {
+  return _listenMode
+}