Unified WinnerSchema (#856)

## Description:

Refactor various types across the project to use WinnerSchema.

## Please complete the following:

- [x] I have added screenshots for all UI updates
- [x] I confirm I have thoroughly tested these changes and take full
responsibility for any bugs introduced
- [x] I understand that submitting code with bugs that could have been
caught through manual testing blocks releases and new features for all
contributors

Co-authored-by: Scott Anderson <662325+scottanderson@users.noreply.github.com>

src/server/GameServer.ts

@@ -562,8 +562,7 @@ export class GameServer {
         this.turns,
         this._startTime ?? 0,
         Date.now(),
-        this.winner?.winner ?? null,
-        this.winner?.winnerType ?? null,
+        this.winner?.winner,
       ),
     );
   }