Quads (#1347)

## Description:

- Add trios and quads
- Add translations for duos, trios, quads
- Add duos, trios, quads to the public lobby rotation
- Increase the frequency of team games


![image](https://github.com/user-attachments/assets/a7bac4e7-9db2-486d-87bc-5779dd64da08)

![image](https://github.com/user-attachments/assets/c1b9225e-2193-4776-b97f-be01a1bdeeed)

## 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
- [x] I understand that submitting code with bugs that could have been
caught through manual testing blocks releases and new features for all
contributors

src/core/configuration/Config.ts

@@ -1,9 +1,8 @@
 import { Colord } from "colord";
 import { JWK } from "jose";
-import { GameConfig, GameID } from "../Schemas";
+import { GameConfig, GameID, TeamCountConfig } from "../Schemas";
 import {
   Difficulty,
-  Duos,
   Game,
   GameMapType,
   GameMode,
@@ -32,7 +31,7 @@ export interface ServerConfig {
   lobbyMaxPlayers(
     map: GameMapType,
     mode: GameMode,
-    numPlayerTeams: number | undefined,
+    numPlayerTeams: TeamCountConfig | undefined,
   ): number;
   numWorkers(): number;
   workerIndex(gameID: GameID): number;
@@ -87,7 +86,7 @@ export interface Config {
   instantBuild(): boolean;
   numSpawnPhaseTurns(): number;
   userSettings(): UserSettings;
-  playerTeams(): number | typeof Duos;
+  playerTeams(): TeamCountConfig;
 
   startManpower(playerInfo: PlayerInfo): number;
   populationIncreaseRate(player: Player | PlayerView): number;

src/core/configuration/DefaultConfig.ts

@@ -2,7 +2,6 @@ import { JWK } from "jose";
 import { z } from "zod/v4";
 import {
   Difficulty,
-  Duos,
   Game,
   GameMapType,
   GameMode,
@@ -20,7 +19,7 @@ import {
 import { TileRef } from "../game/GameMap";
 import { PlayerView } from "../game/GameView";
 import { UserSettings } from "../game/UserSettings";
-import { GameConfig, GameID } from "../Schemas";
+import { GameConfig, GameID, TeamCountConfig } from "../Schemas";
 import { assertNever, simpleHash, within } from "../Util";
 import { Config, GameEnv, NukeMagnitude, ServerConfig, Theme } from "./Config";
 import { PastelTheme } from "./PastelTheme";
@@ -167,13 +166,13 @@ export abstract class DefaultServerConfig implements ServerConfig {
   lobbyMaxPlayers(
     map: GameMapType,
     mode: GameMode,
-    numPlayerTeams: number | undefined,
+    numPlayerTeams: TeamCountConfig | undefined,
   ): number {
     const [l, m, s] = numPlayersConfig[map] ?? [50, 30, 20];
     const r = Math.random();
     const base = r < 0.3 ? l : r < 0.6 ? m : s;
     let p = Math.min(mode === GameMode.Team ? Math.ceil(base * 1.5) : base, l);
-    if (numPlayerTeams !== undefined) {
+    if (typeof numPlayerTeams === "number") {
       p -= p % numPlayerTeams;
     }
     return p;
@@ -279,7 +278,7 @@ export class DefaultConfig implements Config {
   defensePostDefenseBonus(): number {
     return 5;
   }
-  playerTeams(): number | typeof Duos {
+  playerTeams(): TeamCountConfig {
     return this._gameConfig.playerTeams ?? 0;
   }