Resume: exiting a match keeps it alive instead of destroying it

Leaving the table (back button, browser/hardware back) no longer resets the
game — it minimizes it and stays resumable:
- game-store: add `paused` + minimize()/resume(). Single-player (AI) matches
  pause their local timers so nothing happens while away; live (server-run)
  matches keep streaming via the still-active subscription (the .NET GameRoom
  already runs the match to completion and re-broadcasts state on reconnect).
- GameScreen: an unmount effect minimizes any in-progress match no matter how
  you leave; only a finished match (reward dismissed) tears down.
- ResumeGameBar: floating "return to game" pill shown from any screen while a
  match is alive, or while a finished match still has an unseen reward.
- page.tsx: after a full reload, re-enter live mode (minimized) when the server
  re-broadcasts state, and notify when a match you left finishes while away.

Verified: tsc + next build clean; web image rebuilt and serving on :1500.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/components/screens/GameScreen.tsx

@@ -25,11 +25,29 @@ export function GameScreen() {
   const [reward, setReward] = useState<RewardResult | null>(null);
   const submitted = useRef(false);
 
+  // Leaving the table (back button, browser/hardware back) keeps the match alive
+  // & resumable — pause is handled by the unmount effect below. A finished match
+  // is torn down instead.
   const exit = () => {
+    if (useGameStore.getState().game.phase === "match-over") reset();
+    go(returnTo);
+  };
+
+  // Match truly finished (reward dismissed): tear the match down.
+  const finish = () => {
     reset();
     go(returnTo);
   };
 
+  // Any way the table unmounts (exit button, hardware/browser back), keep an
+  // in-progress match alive and resumable instead of letting it run unattended.
+  useEffect(() => {
+    return () => {
+      const gs = useGameStore.getState();
+      if (gs.started && gs.game.phase !== "match-over") gs.minimize();
+    };
+  }, []);
+
   const notifyAchievements = (r: RewardResult) => {
     for (const a of r.newAchievements)
       pushNotification({
@@ -85,7 +103,7 @@ export function GameScreen() {
           won={game.matchWinner === 0}
           onClose={() => {
             setReward(null);
-            exit();
+            finish();
           }}
         />
       )}