update game url to use game code directly

client/src/components/home/CreateGame.tsx

@@ -24,7 +24,7 @@ export default function CreateGame() {
     const game = await createGame(startingSide, unlisted.checked);
 
     if (game) {
-      router.push(`/game/${game.code}`);
+      router.push(`/${game.code}`);
     } else {
       setButtonLoading(false);
       // TODO: Show error message

client/src/components/home/JoinGame.tsx

@@ -31,7 +31,7 @@ export default function JoinGame() {
     const game = await getGame(code);
 
     if (game && game.code) {
-      router.push(`/game/${game.code}`);
+      router.push(`/${game.code}`);
     } else {
       setButtonLoading(false);
       setNotFound(true);

client/src/components/home/PublicGames/JoinButton.tsx

@@ -9,7 +9,7 @@ export default function JoinButton({ code }: { code: string }) {
 
   function handleJoin() {
     startTransition(() => {
-      router.push(`/game/${code}`);
+      router.push(`/${code}`);
     });
   }