feat(playlist): add the Doomsday Clock to the public modifier rotation (#4589)

## Description:

Adds the anti-stall **Doomsday Clock** to the public "special" modifier
rotation, so it rolls into public games like the other spice modifiers,
with a lobby badge.

- `MapPlaylist`: new `isDoomsdayClock` ticket in `SPECIAL_MODIFIER_POOL`
(weight 4, ~20% of special games). When rolled, enables `doomsdayClock`
at a speed picked per game (slow/normal/fast/veryfast).
- `PublicGameModifiers` (type + schema): `isDoomsdayClock` flag drives
the badge.
- `getActiveModifiers` + `en.json`: a "Doomsday Clock" badge/label.
- Test covering the badge wiring.

## Please complete the following:

- [x] I have added screenshots for all UI updates
- [x] I process any text displayed to the user through translateText()
and I've added it to the en.json file
- [x] I have added relevant tests to the test directory

src/client/Utils.ts

@@ -220,6 +220,12 @@ export function getActiveModifiers(
       badgeKey: "public_game_modifier.water_nukes",
     });
   }
+  if (modifiers.isDoomsdayClock) {
+    result.push({
+      labelKey: "public_game_modifier.doomsday_clock_label",
+      badgeKey: "public_game_modifier.doomsday_clock",
+    });
+  }
   return result;
 }