feat: include publicID in admin-bot live stats players (#4404)

## Description:

The live stats endpoint enriches each player with username/connected but
not publicId, so an account-keyed caller (e.g. an admin bot, which knows
players by account, not per-session clientID) can't map a stats row back
to a player directly. Add publicId from the same activeClients source —
mirrors the kick_player targetPublicID path.

## 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

## Please put your Discord username so you can be contacted if a bug or
regression is found:

zixer._

src/server/GameServer.ts

@@ -1419,6 +1419,7 @@ export class GameServer {
     turn: number;
     players: (PlayerLiveStats & {
       username: string | null;
+      publicID: string | null;
       connected: boolean;
     })[];
   } | null {
@@ -1427,11 +1428,15 @@ export class GameServer {
     }
     return {
       turn: this.latestLiveStats.turn,
-      players: this.latestLiveStats.players.map((p) => ({
-        ...p,
-        username: this.allClients.get(p.clientID)?.username ?? null,
-        connected: !this.isClientDisconnected(p.clientID),
-      })),
+      players: this.latestLiveStats.players.map((p) => {
+        const client = this.allClients.get(p.clientID);
+        return {
+          ...p,
+          username: client?.username ?? null,
+          publicID: client?.publicId ?? null,
+          connected: !this.isClientDisconnected(p.clientID),
+        };
+      }),
     };
   }
 }