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/mock/data.ts

@@ -43,10 +43,9 @@ export const PROFILE: Profile = {
 
 // Seed social/account data for the mock (pnpm start + Playwright). The mock profile
 // is a durable account so the Stage 8 surfaces (friends, stats, history) are reachable.
-export const MOCK_FRIENDS: AccountRef[] = [
-  { accountId: 'ann', displayName: 'Ann' },
-  { accountId: 'kaya', displayName: 'Kaya' },
-];
+// Ann is the active game's opponent but deliberately not a friend, so the in-game
+// "add to friends" flow is demonstrable; Kaya (a finished-game opponent) is the friend.
+export const MOCK_FRIENDS: AccountRef[] = [{ accountId: 'kaya', displayName: 'Kaya' }];
 
 export const MOCK_INCOMING: AccountRef[] = [{ accountId: 'rick', displayName: 'Rick' }];
 
@@ -144,6 +143,7 @@ function activeGame(): MockGame {
       turnTimeoutSecs: 86400,
       moveCount: G1_MOVES.length,
       endReason: '',
+      lastActivityUnix: Math.floor(Date.now() / 1000) - 7200,
       seats: [seat(0, ME, 'You', 19), seat(1, 'ann', 'Ann', 13)],
     },
     moves: G1_MOVES,
@@ -177,6 +177,7 @@ function finishedG2(): MockGame {
       turnTimeoutSecs: 86400,
       moveCount: 2,
       endReason: 'normal',
+      lastActivityUnix: Math.floor(Date.now() / 1000) - 86400,
       seats: [seat(0, ME, 'You', 320, true), seat(1, 'kaya', 'Kaya', 281)],
     },
     moves: [
@@ -211,6 +212,7 @@ function finishedG3(): MockGame {
       turnTimeoutSecs: 86400,
       moveCount: 1,
       endReason: 'resignation',
+      lastActivityUnix: Math.floor(Date.now() / 1000) - 172800,
       seats: [seat(0, ME, 'You', 150), seat(1, 'rick', 'Rick', 212, true)],
     },
     moves: [