feat(#87): [Live] Correct FP/Q timing truth, hierarchy, and mobile navigation

Implemented by claude via .agents/dev dispatch.

frontend/src/components/Nav.tsx

@@ -1,6 +1,17 @@
 import { Link } from '@tanstack/react-router'
+import { useQuery } from '@tanstack/react-query'
+import { fetchLiveState } from '../api'
+import { isLiveSessionActive } from '../lib/live'
 
 export function Nav() {
+  const { data: liveState } = useQuery({
+    queryKey: ['live-state'],
+    queryFn: fetchLiveState,
+    staleTime: 5_000,
+    refetchInterval: 30_000,
+  })
+  const liveActive = isLiveSessionActive(liveState)
+
   return (
     <nav className="app-nav">
       <Link to="/" className="nav-logo">
@@ -10,8 +21,16 @@ export function Nav() {
         <Link to="/" activeProps={{ className: 'active' }} activeOptions={{ exact: true }}>
           Command
         </Link>
-        <Link to="/live" activeProps={{ className: 'active' }}>
+        <Link
+          to="/live"
+          className={liveActive ? 'nav-live nav-live-on' : 'nav-live'}
+          activeProps={{ className: 'active' }}
+          data-testid="nav-live"
+          data-live-active={liveActive ? 'true' : 'false'}
+        >
+          {liveActive && <span className="nav-live-dot" aria-hidden="true" />}
           Live
+          {liveActive && <span className="sr-only"> session active</span>}
         </Link>
         <Link to="/race-hub" search={{}} activeProps={{ className: 'active' }}>
           Race Hub