feat(social): per-game friend request to disguised robots + lobby/stats/tile cosmetics

Functional: the in-game add-friend handshake aimed at an auto-match opponent who is
secretly a pooled robot now records the request per (game, seat) in a new
robot_friend_requests table -- never against the shared robot account -- mirroring the
robot_blocks pattern. The shared account stays out of friendships, the "requested" state
is pinned to the seat (not leaked across the player's other games), the robot ignores it,
and a background reaper drops the row 7 days after its game finishes. The outgoing-requests
list carries these per-game rows so the seat control stays disabled across reloads. No
withdraw UI, per owner decision.

Cosmetics:
- Lobby: an in-progress game tints the viewer's own score number green when leading or
  tied, red when trailing (reusing --ok/--danger); scores now render in seat-number order,
  matching the over-the-board scoreboard.
- Stats: the per-variant best move is laid out on two lines -- the variant label, then the
  score (right-aligned in its column) and the word tiles (left-aligned) below it.
- Dark theme: the played-tile background is a touch darker so a player-placed tile reads
  with more contrast (light theme unchanged).

Docs (ARCHITECTURE, FUNCTIONAL + _ru mirror, backend README, UI_DESIGN) updated in the
same change.

gateway/internal/transcode/transcode_social.go

@@ -93,7 +93,9 @@ func friendsOutgoingHandler(backend *backendclient.Client) Handler {
 func friendRequestHandler(backend *backendclient.Client) Handler {
 	return func(ctx context.Context, req Request) ([]byte, error) {
 		in := fb.GetRootAsTargetRequest(req.Payload, 0)
-		if err := backend.SendFriendRequest(ctx, req.UserID, string(in.AccountId())); err != nil {
+		// game_id is set only by an in-game request, so a disguised-robot opponent is recorded
+		// per-game; it is empty for any non-game path.
+		if err := backend.SendFriendRequest(ctx, req.UserID, string(in.AccountId()), string(in.GameId())); err != nil {
 			return nil, err
 		}
 		return encodeAck(true), nil