have lobby schedule ffa, teams, & special game types (#3196)

## Description:

This implements the backend for multiple lobbies in preparation for
https://github.com/openfrontio/OpenFrontIO/pull/3191

The server now schedules & sends a map of game type (ffa, teams,
special) => public lobbies.

NOTE: this is just temporary, the lobby only shows ffa currently.

Have the Master scheduler schedule ffa, teams, & special games. 

## 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:

evan

src/core/Schemas.ts

@@ -139,6 +139,9 @@ export type GameStartInfo = z.infer<typeof GameStartInfoSchema>;
 export type GameInfo = z.infer<typeof GameInfoSchema>;
 export type PublicGames = z.infer<typeof PublicGamesSchema>;
 export type PublicGameInfo = z.infer<typeof PublicGameInfoSchema>;
+export type PublicGameType = z.infer<typeof PublicGameTypeSchema>;
+
+export const PublicGameTypeSchema = z.enum(["ffa", "team", "special"]);
 
 const ClientInfoSchema = z.object({
   clientID: z.string(),
@@ -152,6 +155,7 @@ export const GameInfoSchema = z.object({
   startsAt: z.number().optional(),
   serverTime: z.number(),
   gameConfig: z.lazy(() => GameConfigSchema).optional(),
+  publicGameType: PublicGameTypeSchema.optional(),
 });
 
 export const PublicGameInfoSchema = z.object({
@@ -159,11 +163,12 @@ export const PublicGameInfoSchema = z.object({
   numClients: z.number(),
   startsAt: z.number(),
   gameConfig: z.lazy(() => GameConfigSchema).optional(),
+  publicGameType: PublicGameTypeSchema,
 });
 
 export const PublicGamesSchema = z.object({
   serverTime: z.number(),
-  games: PublicGameInfoSchema.array(),
+  games: z.record(PublicGameTypeSchema, z.array(PublicGameInfoSchema)),
 });
 
 export class LobbyInfoEvent implements GameEvent {