Delayed lobby start (#4184)

Resolves #4169

## Description:

Adds a delayed lobby start option.
Utilizes the same system as for public lobbies.
The default for the option is for lobbies to take 3 seconds to start,
however this can easily be changed.

The current setting is controlled through an enable-disable slider,
however there are multiple other options for how to control this.
For example we could do a slider, an input field, a dropdown etc. And i
dont necessarily know if the currently implemented option is the best.

Furhtermore im not sure if i have used the language file completely
correctly. There is now a duplicate field for both private and public
lobby. However there is not category shared between the two. So i
decided to reuse the field from public for private games, as this
simplified the code a bit.

**Host video**

https://github.com/user-attachments/assets/6f3db6e4-7323-4fad-8544-efb8cef4d969

**Non-host video**

https://github.com/user-attachments/assets/ee02a072-1f42-4dde-a5d9-120fda862eb7

## 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:
FrederikJA

src/server/GameServer.ts

@@ -149,6 +149,9 @@ export class GameServer {
     if (gameConfig.maxTimerValue !== undefined) {
       this.gameConfig.maxTimerValue = gameConfig.maxTimerValue ?? undefined;
     }
+    if (gameConfig.startDelay !== undefined) {
+      this.gameConfig.startDelay = gameConfig.startDelay ?? undefined;
+    }
     if (gameConfig.instantBuild !== undefined) {
       this.gameConfig.instantBuild = gameConfig.instantBuild;
     }
@@ -488,7 +491,7 @@ export class GameServer {
                 this.updateGameConfig(stampedIntent.config);
                 return;
               }
-              case "start_game": {
+              case "toggle_game_start_timer": {
                 if (client.clientID !== this.lobbyCreatorID) {
                   this.log.warn(`Only lobby creator can start game`, {
                     clientID: client.clientID,
@@ -514,7 +517,13 @@ export class GameServer {
                   creatorID: client.clientID,
                   gameID: this.id,
                 });
-                this.start();
+                if (this.startsAt) {
+                  this.startsAt = undefined;
+                } else {
+                  this.setStartsAt(
+                    Date.now() + (this.gameConfig.startDelay ?? 0) * 1000,
+                  );
+                }
                 return;
               }
               case "toggle_pause": {
@@ -931,25 +940,6 @@ export class GameServer {
     const noRecentPings = now > this.lastPingUpdate + 20 * 1000;
     const noActive = this.activeClients.length === 0;
 
-    if (this.gameConfig.gameType !== GameType.Public) {
-      if (this._hasStarted) {
-        if (noActive && noRecentPings) {
-          this.log.info("private game complete", {
-            gameID: this.id,
-          });
-          return GamePhase.Finished;
-        } else {
-          return GamePhase.Active;
-        }
-      } else if (this._hasEnded) {
-        return GamePhase.Finished;
-      } else {
-        return GamePhase.Lobby;
-      }
-    }
-
-    // Public Games
-
     const lessThanLifetime = this.startsAt ? Date.now() < this.startsAt : true;
     if (
       lessThanLifetime &&