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/encode_social.go

@@ -50,12 +50,36 @@ func encodeIncomingList(r backendclient.IncomingListResp) []byte {
 	return b.FinishedBytes()
 }
 
+// buildRobotFriendVector builds the OutgoingRequestList robots vector (per-game
+// disguised-robot friend requests).
+func buildRobotFriendVector(b *flatbuffers.Builder, robots []backendclient.RobotFriendReqResp) flatbuffers.UOffsetT {
+	offs := make([]flatbuffers.UOffsetT, len(robots))
+	for i, r := range robots {
+		id := b.CreateString(r.ID)
+		name := b.CreateString(r.DisplayName)
+		gid := b.CreateString(r.GameID)
+		fb.RobotFriendRefStart(b)
+		fb.RobotFriendRefAddId(b, id)
+		fb.RobotFriendRefAddDisplayName(b, name)
+		fb.RobotFriendRefAddGameId(b, gid)
+		fb.RobotFriendRefAddSeat(b, int32(r.Seat))
+		offs[i] = fb.RobotFriendRefEnd(b)
+	}
+	fb.OutgoingRequestListStartRobotsVector(b, len(offs))
+	for i := len(offs) - 1; i >= 0; i-- {
+		b.PrependUOffsetT(offs[i])
+	}
+	return b.EndVector(len(offs))
+}
+
 // encodeOutgoingList builds an OutgoingRequestList payload.
 func encodeOutgoingList(r backendclient.OutgoingListResp) []byte {
 	b := flatbuffers.NewBuilder(256)
 	v := buildAccountRefVector(b, r.Requests, fb.OutgoingRequestListStartRequestsVector)
+	rv := buildRobotFriendVector(b, r.Robots)
 	fb.OutgoingRequestListStart(b)
 	fb.OutgoingRequestListAddRequests(b, v)
+	fb.OutgoingRequestListAddRobots(b, rv)
 	b.Finish(fb.OutgoingRequestListEnd(b))
 	return b.FinishedBytes()
 }