Put friends on the same team (#3994)

Fixes #3911

## Description:

- Server captures `publicId` and `friends` from `getUserMe()` and
includes each player's in-game friend `clientID`s in `PlayerSchema` on
game start
- Team assignment treats friends as a **soft preference** (best-effort):
a non-clan player goes to the team where the most of their friends
already are; if that team is full they spill to the next-emptiest team
rather than getting kicked
- Clans remain strict (kick overflow) since clan membership is an
explicit opt-in; friends are implicit, so a friend-of-friend chain that
doesn't fit shouldn't bench anyone
- Friendship is symmetric — an edge from either direction counts, which
keeps things working when one side's `getUserMe` is stale
- Lobby preview unchanged — friend grouping only takes effect once the
game actually starts (avoids exposing friend lists in the lobby payload)


## 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/server/GameServer.ts

@@ -731,18 +731,29 @@ export class GameServer {
     // if no client connects/pings.
     this.lastPingUpdate = Date.now();
 
+    const publicIdToClientID = new Map<string, ClientID>();
+    for (const c of this.activeClients) {
+      if (c.publicId) publicIdToClientID.set(c.publicId, c.clientID);
+    }
+
     const result = GameStartInfoSchema.safeParse({
       gameID: this.id,
       lobbyCreatedAt: this.createdAt,
       visibleAt: this.visibleAt,
       config: this.gameConfig,
-      players: this.activeClients.map((c) => ({
-        username: c.username,
-        clanTag: c.clanTag ?? null,
-        clientID: c.clientID,
-        cosmetics: c.cosmetics,
-        isLobbyCreator: this.lobbyCreatorID === c.clientID,
-      })),
+      players: this.activeClients.map((c) => {
+        const friendClientIDs = c.friends
+          .map((pid) => publicIdToClientID.get(pid))
+          .filter((id): id is ClientID => id !== undefined);
+        return {
+          username: c.username,
+          clanTag: c.clanTag ?? null,
+          clientID: c.clientID,
+          cosmetics: c.cosmetics,
+          isLobbyCreator: this.lobbyCreatorID === c.clientID,
+          friends: friendClientIDs.length > 0 ? friendClientIDs : undefined,
+        };
+      }),
     });
     if (!result.success) {
       const error = z.prettifyError(result.error);