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.

backend/internal/social/robotfriends.go

@@ -0,0 +1,175 @@
+package social
+
+import (
+	"context"
+	"fmt"
+	"slices"
+	"time"
+
+	"github.com/google/uuid"
+	"go.uber.org/zap"
+)
+
+// robotFriendRequestTTL is how long a per-game disguised-robot friend request is kept
+// after its game has finished before the reaper deletes it. It is a sibling of
+// friendRequestTTL; the request is housekeeping for the in-game "request sent" state,
+// so it is purged once the finished game is well past its lobby lifetime.
+const robotFriendRequestTTL = 7 * 24 * time.Hour
+
+// robotFriendRequestReapInterval is how often the reaper sweeps expired rows.
+const robotFriendRequestReapInterval = time.Hour
+
+// RobotFriendRequest is one per-game friend request to a disguised-robot opponent: the
+// row id, the game name the player saw, and the game + seat it was sent in (so the
+// in-game scoreboard can re-mark that seat as already requested).
+type RobotFriendRequest struct {
+	ID          uuid.UUID
+	DisplayName string
+	GameID      uuid.UUID
+	Seat        int
+}
+
+// RequestInGame sends a friend request to addresseeID for requesterID from within gameID.
+// A human is requested normally (the friendships table, via SendFriendRequest). A
+// disguised-robot opponent is instead recorded per-game in robot_friend_requests — never
+// the shared robot account — so the matchmaker keeps robots free, the same robot stays
+// un-requested in the requester's other games (under its other names), and the in-game
+// "request sent" state is pinned to this seat rather than the shared account. The robot
+// ignores the request (it never becomes a friendship); the reaper deletes the row once
+// the game is long finished. It is the entry point for the in-game add-friend control;
+// the friend-code path goes elsewhere.
+func (svc *Service) RequestInGame(ctx context.Context, requesterID, addresseeID, gameID uuid.UUID) error {
+	if requesterID == addresseeID {
+		return ErrSelfRelation
+	}
+	isRobot, err := svc.accounts.IsRobot(ctx, addresseeID)
+	if err != nil {
+		return err
+	}
+	if !isRobot {
+		return svc.SendFriendRequest(ctx, requesterID, addresseeID)
+	}
+	if gameID == uuid.Nil {
+		return ErrNotParticipant
+	}
+	seats, _, _, err := svc.games.Participants(ctx, gameID)
+	if err != nil {
+		return err
+	}
+	seat := slices.Index(seats, addresseeID)
+	if seat < 0 {
+		return ErrNotParticipant
+	}
+	name, _ := svc.games.SeatName(ctx, gameID, addresseeID)
+	return svc.store.insertRobotFriendRequest(ctx, requesterID, gameID, seat, addresseeID, name)
+}
+
+// ListRobotFriendRequests returns requesterID's per-game disguised-robot friend
+// requests, newest first.
+func (svc *Service) ListRobotFriendRequests(ctx context.Context, requesterID uuid.UUID) ([]RobotFriendRequest, error) {
+	return svc.store.listRobotFriendRequests(ctx, requesterID)
+}
+
+// insertRobotFriendRequest records a per-game robot friend request; a duplicate (same
+// requester, game, seat) is ignored.
+func (s *Store) insertRobotFriendRequest(ctx context.Context, requester, gameID uuid.UUID, seat int, robotID uuid.UUID, name string) error {
+	id, err := uuid.NewV7()
+	if err != nil {
+		return fmt.Errorf("social: new robot friend request id: %w", err)
+	}
+	const q = `INSERT INTO backend.robot_friend_requests (id, requester_id, game_id, seat, robot_id, display_name)
+VALUES ($1, $2, $3, $4, $5, $6)
+ON CONFLICT (requester_id, game_id, seat) DO NOTHING`
+	if _, err := s.db.ExecContext(ctx, q, id, requester, gameID, int16(seat), robotID, name); err != nil {
+		return fmt.Errorf("social: insert robot friend request: %w", err)
+	}
+	return nil
+}
+
+// listRobotFriendRequests returns requester's robot friend requests, newest first.
+func (s *Store) listRobotFriendRequests(ctx context.Context, requester uuid.UUID) ([]RobotFriendRequest, error) {
+	const q = `SELECT id, display_name, game_id, seat FROM backend.robot_friend_requests
+WHERE requester_id = $1 ORDER BY created_at DESC`
+	rows, err := s.db.QueryContext(ctx, q, requester)
+	if err != nil {
+		return nil, fmt.Errorf("social: list robot friend requests: %w", err)
+	}
+	defer rows.Close()
+	var out []RobotFriendRequest
+	for rows.Next() {
+		var r RobotFriendRequest
+		var seat int16
+		if err := rows.Scan(&r.ID, &r.DisplayName, &r.GameID, &seat); err != nil {
+			return nil, fmt.Errorf("social: scan robot friend request: %w", err)
+		}
+		r.Seat = int(seat)
+		out = append(out, r)
+	}
+	return out, rows.Err()
+}
+
+// ReapExpiredRobotFriendRequests deletes every per-game robot friend request whose game has
+// been finished for longer than robotFriendRequestTTL, reporting how many rows were removed.
+// Rows for active (not-yet-finished) games are kept so the in-game "request sent" state
+// survives. It backs the RobotFriendRequestReaper and is directly callable in tests.
+func (svc *Service) ReapExpiredRobotFriendRequests(ctx context.Context) (int64, error) {
+	return svc.store.deleteExpiredRobotFriendRequests(ctx, svc.now().Add(-robotFriendRequestTTL))
+}
+
+// deleteExpiredRobotFriendRequests removes robot friend requests whose game has been
+// finished since before cutoff, reporting how many rows were deleted.
+func (s *Store) deleteExpiredRobotFriendRequests(ctx context.Context, cutoff time.Time) (int64, error) {
+	const q = `DELETE FROM backend.robot_friend_requests r
+USING backend.games g
+WHERE r.game_id = g.game_id AND g.status = 'finished' AND g.finished_at < $1`
+	res, err := s.db.ExecContext(ctx, q, cutoff)
+	if err != nil {
+		return 0, fmt.Errorf("social: delete expired robot friend requests: %w", err)
+	}
+	n, err := res.RowsAffected()
+	if err != nil {
+		return 0, fmt.Errorf("social: delete expired robot friend requests rows: %w", err)
+	}
+	return n, nil
+}
+
+// RobotFriendRequestReaper periodically reaps expired per-game disguised-robot friend
+// requests via Service.ReapExpiredRobotFriendRequests. It mirrors the account.GuestReaper:
+// one background goroutine, started once from main.
+type RobotFriendRequestReaper struct {
+	svc *Service
+	log *zap.Logger
+}
+
+// NewRobotFriendRequestReaper constructs a reaper over svc. log may be nil.
+func NewRobotFriendRequestReaper(svc *Service, log *zap.Logger) *RobotFriendRequestReaper {
+	if log == nil {
+		log = zap.NewNop()
+	}
+	return &RobotFriendRequestReaper{svc: svc, log: log}
+}
+
+// Interval is the reaper's sweep cadence, for the startup log line.
+func (r *RobotFriendRequestReaper) Interval() time.Duration { return robotFriendRequestReapInterval }
+
+// Retention is the reaper's post-finish retention window, for the startup log line.
+func (r *RobotFriendRequestReaper) Retention() time.Duration { return robotFriendRequestTTL }
+
+// Run reaps expired robot friend requests on each tick until ctx is cancelled.
+func (r *RobotFriendRequestReaper) Run(ctx context.Context) {
+	ticker := time.NewTicker(robotFriendRequestReapInterval)
+	defer ticker.Stop()
+	for {
+		select {
+		case <-ctx.Done():
+			return
+		case <-ticker.C:
+			n, err := r.svc.ReapExpiredRobotFriendRequests(ctx)
+			if err != nil {
+				r.log.Warn("robot friend request reap failed", zap.Error(err))
+			} else if n > 0 {
+				r.log.Info("reaped expired robot friend requests", zap.Int64("count", n))
+			}
+		}
+	}
+}