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/backendclient/api_social.go

@@ -26,9 +26,20 @@ type IncomingListResp struct {
 }
 
 // OutgoingListResp is the addressees the caller has already requested (a live pending
-// request or one the addressee declined) and cannot re-request.
+// request or one the addressee declined) and cannot re-request, plus the per-game
+// disguised-robot requests (not real accounts).
 type OutgoingListResp struct {
-	Requests []AccountRefResp `json:"requests"`
+	Requests []AccountRefResp     `json:"requests"`
+	Robots   []RobotFriendReqResp `json:"robots"`
+}
+
+// RobotFriendReqResp is one per-game disguised-robot friend request: the row id, the game
+// name the player saw, and the game + seat it was sent in.
+type RobotFriendReqResp struct {
+	ID          string `json:"id"`
+	DisplayName string `json:"display_name"`
+	GameID      string `json:"game_id"`
+	Seat        int    `json:"seat"`
 }
 
 // FriendCodeResp is a freshly issued one-time friend code.
@@ -137,10 +148,12 @@ type InvitationParams struct {
 
 // --- friends ---
 
-// SendFriendRequest sends a friend request to a played opponent.
-func (c *Client) SendFriendRequest(ctx context.Context, userID, targetID string) error {
+// SendFriendRequest sends a friend request to a played opponent. A non-empty gameID
+// marks an in-game request, so a disguised-robot opponent is recorded as a per-game
+// request; it is empty for any non-game path.
+func (c *Client) SendFriendRequest(ctx context.Context, userID, targetID, gameID string) error {
 	return c.do(ctx, http.MethodPost, "/api/v1/user/friends/request", userID, "",
-		map[string]string{"account_id": targetID}, nil)
+		map[string]string{"account_id": targetID, "game_id": gameID}, nil)
 }
 
 // RespondFriendRequest accepts or declines an incoming request.