fix: stamp lastSavedAt into game state blob on save

apps/api/src/routes/game.ts

@@ -367,6 +367,13 @@ gameRouter.post("/save", async (context) => {
 
   const now = Date.now();
 
+  // Stamp the authoritative save timestamp into the state blob so that on the
+  // next load the client reads the correct value from state.player.lastSavedAt.
+  stateToSave = {
+    ...stateToSave,
+    player: { ...stateToSave.player, lastSavedAt: now },
+  };
+
   await prisma.player.update({
     where: { discordId },
     data: {