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.

ui/src/lib/mock/client.ts

@@ -29,6 +29,7 @@ import type {
   LinkResult,
   MatchResult,
   MoveResult,
+  OutgoingList,
   Profile,
   ProfileUpdate,
   PushEvent,
@@ -527,10 +528,11 @@ export class MockGateway implements GatewayClient {
   async friendsIncoming(): Promise<AccountRef[]> {
     return this.incoming.map((f) => ({ ...f }));
   }
-  async friendsOutgoing(): Promise<AccountRef[]> {
-    return this.outgoing.map((f) => ({ ...f }));
+  async friendsOutgoing(): Promise<OutgoingList> {
+    // The mock models human outgoing requests only (no disguised robots); robots stays empty.
+    return { requests: this.outgoing.map((f) => ({ ...f })), robots: [] };
   }
-  async friendRequest(accountId: string): Promise<void> {
+  async friendRequest(accountId: string, _gameId?: string): Promise<void> {
     // The real backend requires a shared game; the mock records the outgoing request so
     // the game's "add to friends" item reads as sent across reloads.
     if (!this.outgoing.some((o) => o.accountId === accountId)) {