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.

gateway/internal/transcode/transcode_test.go

@@ -158,7 +158,7 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/games" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"english","status":"active","players":2,"to_move":0,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}]}`))
+		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"english","status":"active","players":2,"to_move":0,"last_activity_unix":1717000000,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}]}`))
 	})
 	defer cleanup()
 
@@ -177,6 +177,9 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 	if string(g.Id()) != "g-1" {
 		t.Errorf("game id = %q, want g-1", g.Id())
 	}
+	if g.LastActivityUnix() != 1717000000 {
+		t.Errorf("last activity = %d, want 1717000000", g.LastActivityUnix())
+	}
 	var seat fb.SeatView
 	g.Seats(&seat, 1)
 	if string(seat.DisplayName()) != "Ann" {