Improve UX with merged run view, method badges, grouped encounters, and mobile nav

Merges the run dashboard into the encounters page as a unified view at /runs/:runId,
adds encounter method grouping in the modal and badges on route rows, improves the
home page with recent runs, adds mobile hamburger nav, and polishes empty states.

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

frontend/src/pages/NewRun.tsx

@@ -17,6 +17,10 @@ export function NewRun() {
   const [runName, setRunName] = useState('')
 
   const handleGameSelect = (game: Game) => {
+    if (selectedGame?.id === game.id) {
+      setSelectedGame(null)
+      return
+    }
     setSelectedGame(game)
     if (!runName || runName === `${selectedGame?.name} Nuzlocke`) {
       setRunName(`${game.name} Nuzlocke`)