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/inttest/robot_friend_test.go

@@ -0,0 +1,82 @@
+//go:build integration
+
+package inttest
+
+import (
+	"context"
+	"testing"
+	"time"
+
+	"github.com/google/uuid"
+
+	"scrabble/backend/internal/account"
+	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/game"
+)
+
+// TestRobotFriendRequestIsPerGameAndReaped checks that sending a friend request to a
+// disguised-robot opponent is recorded per-game in robot_friend_requests — never in the
+// friendships table or against the shared robot account — that a re-send is idempotent, and
+// that the reaper deletes the row once its game has been finished past the retention window
+// while keeping the row for an active game.
+func TestRobotFriendRequestIsPerGameAndReaped(t *testing.T) {
+	ctx := context.Background()
+	svc := newSocialService()
+	accs := account.NewStore(testDB)
+	human := provisionAccount(t)
+	robot, err := accs.ProvisionRobot(ctx, "robot-friend-"+uuid.NewString(), "Robbie")
+	if err != nil {
+		t.Fatalf("provision robot: %v", err)
+	}
+	g, err := newGameService().Create(ctx, game.CreateParams{
+		Variant: engine.VariantEnglish, Seats: []uuid.UUID{human, robot.ID},
+		TurnTimeout: 24 * time.Hour, Seed: openingSeed(t),
+	})
+	if err != nil {
+		t.Fatalf("create game: %v", err)
+	}
+
+	if err := svc.RequestInGame(ctx, human, robot.ID, g.ID); err != nil {
+		t.Fatalf("request robot: %v", err)
+	}
+	rfr, err := svc.ListRobotFriendRequests(ctx, human)
+	if err != nil {
+		t.Fatalf("list robot friend requests: %v", err)
+	}
+	if len(rfr) != 1 || rfr[0].GameID != g.ID || rfr[0].Seat != 1 {
+		t.Fatalf("robot friend requests = %v, want one for game %s seat 1", rfr, g.ID)
+	}
+	// The friendships table must stay empty: no outgoing request against the shared robot account.
+	if out, _ := svc.ListOutgoingRequests(ctx, human); len(out) != 0 {
+		t.Errorf("friendships outgoing must be empty for a robot request, got %v", out)
+	}
+
+	// A re-send to the same game+seat is idempotent (the UNIQUE constraint collapses it).
+	if err := svc.RequestInGame(ctx, human, robot.ID, g.ID); err != nil {
+		t.Fatalf("re-request robot: %v", err)
+	}
+	if rfr, _ := svc.ListRobotFriendRequests(ctx, human); len(rfr) != 1 {
+		t.Fatalf("re-request must not duplicate, got %v", rfr)
+	}
+
+	// While the game is active the reaper keeps the row.
+	if n, err := svc.ReapExpiredRobotFriendRequests(ctx); err != nil || n != 0 {
+		t.Fatalf("reap on active game = (%d, %v), want (0, nil)", n, err)
+	}
+	if rfr, _ := svc.ListRobotFriendRequests(ctx, human); len(rfr) != 1 {
+		t.Fatalf("active-game request must survive the reaper, got %v", rfr)
+	}
+
+	// Finish the game well past the retention window: the reaper now deletes the row.
+	finished := time.Now().UTC().Add(-8 * 24 * time.Hour)
+	if _, err := testDB.ExecContext(ctx,
+		`UPDATE backend.games SET status='finished', finished_at=$1 WHERE game_id=$2`, finished, g.ID); err != nil {
+		t.Fatalf("finish game: %v", err)
+	}
+	if n, err := svc.ReapExpiredRobotFriendRequests(ctx); err != nil || n != 1 {
+		t.Fatalf("reap on long-finished game = (%d, %v), want (1, nil)", n, err)
+	}
+	if rfr, _ := svc.ListRobotFriendRequests(ctx, human); len(rfr) != 0 {
+		t.Errorf("long-finished request not reaped: %v", rfr)
+	}
+}