lobby fill time added to stats (#2382)

## Description:

Finishes & closes #1969 and closes #1806.

## 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
- [x] I confirm I have thoroughly tested these changes and take full
responsibility for any bugs introduced

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

w.o.n

---------

Co-authored-by: Evan <evanpelle@gmail.com>

src/server/GameServer.ts

@@ -401,6 +401,7 @@ export class GameServer {
 
     const result = GameStartInfoSchema.safeParse({
       gameID: this.id,
+      lobbyCreatedAt: this.createdAt,
       config: this.gameConfig,
       players: this.activeClients.map((c) => ({
         username: c.username,
@@ -439,6 +440,7 @@ export class GameServer {
           type: "start",
           turns: this.turns.slice(lastTurn),
           gameStartInfo: this.gameStartInfo,
+          lobbyCreatedAt: this.createdAt,
         } satisfies ServerStartGameMessage),
       );
     } catch (error) {
@@ -706,6 +708,7 @@ export class GameServer {
           this._startTime ?? 0,
           Date.now(),
           this.winner?.winner,
+          this.createdAt,
         ),
       ),
     );