Stage 17 round 6 (#16/#17, PR C): lobby sort + server-derived in-game friend state

Lobby: group the my-games list into your-turn / opponent-turn / finished
(empty sections hidden), ordered by last activity (your-turn oldest-first,
the other two newest-first), as a compact line-separated list. gameDTO and
FB GameView gain last_activity_unix (turn start while active, finish time
once finished); a pure lib/lobbysort.ts holds the grouping/ordering.

Friends: the in-game 'add to friends' item is now server-derived via a new
GET /user/friends/outgoing (+ friends.outgoing op), returning addressees with
a pending OR declined request (both read as 'request sent'), so it is correct
across reloads; it shows a disabled '✓ in friends' once accepted. It
live-updates when the opponent answers: RespondFriendRequest now publishes
friend_added (accept) / friend_declined (new notify sub-kind, decline) to the
original requester, whose open game re-derives its friend state.

Tests: lobbysort unit test; gateway outgoing + last_activity transcode tests;
backend integration ListOutgoingRequests + respond-publishes-to-requester;
e2e updated for the new lobby section labels + a non-friend active opponent.
Docs: ARCHITECTURE notify catalog, FUNCTIONAL(+ru) lobby/friends, PLAN.

ui/src/lib/lobbysort.test.ts

@@ -0,0 +1,68 @@
+import { describe, expect, it } from 'vitest';
+import { groupGames, isMyTurn } from './lobbysort';
+import type { GameView, Seat } from './model';
+
+const ME = 'me';
+const seat = (s: number, accountId: string): Seat => ({
+  seat: s,
+  accountId,
+  displayName: accountId,
+  score: 0,
+  hintsUsed: 0,
+  isWinner: false,
+});
+
+function game(id: string, status: GameView['status'], toMove: number, lastActivityUnix: number): GameView {
+  return {
+    id,
+    variant: 'english',
+    dictVersion: 'v1',
+    status,
+    players: 2,
+    toMove,
+    turnTimeoutSecs: 0,
+    moveCount: 0,
+    endReason: '',
+    lastActivityUnix,
+    seats: [seat(0, ME), seat(1, 'opp')],
+  };
+}
+
+describe('groupGames', () => {
+  it('partitions into your-turn, their-turn and finished', () => {
+    const g = groupGames(
+      [
+        game('a', 'active', 0, 100), // toMove 0 == my seat -> my turn
+        game('b', 'active', 1, 100), // their turn
+        game('c', 'finished', 0, 100),
+      ],
+      ME,
+    );
+    expect(g.yourTurn.map((x) => x.id)).toEqual(['a']);
+    expect(g.theirTurn.map((x) => x.id)).toEqual(['b']);
+    expect(g.finished.map((x) => x.id)).toEqual(['c']);
+  });
+
+  it('orders your-turn oldest-first, the other two newest-first', () => {
+    const g = groupGames(
+      [
+        game('y_new', 'active', 0, 200),
+        game('y_old', 'active', 0, 100),
+        game('t_new', 'active', 1, 200),
+        game('t_old', 'active', 1, 100),
+        game('f_new', 'finished', 0, 200),
+        game('f_old', 'finished', 0, 100),
+      ],
+      ME,
+    );
+    expect(g.yourTurn.map((x) => x.id)).toEqual(['y_old', 'y_new']);
+    expect(g.theirTurn.map((x) => x.id)).toEqual(['t_new', 't_old']);
+    expect(g.finished.map((x) => x.id)).toEqual(['f_new', 'f_old']);
+  });
+
+  it('isMyTurn is false for a finished game even at my seat', () => {
+    expect(isMyTurn(game('x', 'finished', 0, 0), ME)).toBe(false);
+    expect(isMyTurn(game('x', 'active', 0, 0), ME)).toBe(true);
+    expect(isMyTurn(game('x', 'active', 1, 0), ME)).toBe(false);
+  });
+});