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/backendclient/api_social.go

@@ -25,6 +25,12 @@ type IncomingListResp struct {
 	Requests []AccountRefResp `json:"requests"`
 }
 
+// OutgoingListResp is the addressees the caller has already requested (a live pending
+// request or one the addressee declined) and cannot re-request.
+type OutgoingListResp struct {
+	Requests []AccountRefResp `json:"requests"`
+}
+
 // FriendCodeResp is a freshly issued one-time friend code.
 type FriendCodeResp struct {
 	Code          string `json:"code"`
@@ -134,6 +140,14 @@ func (c *Client) ListIncoming(ctx context.Context, userID string) (IncomingListR
 	return out, err
 }
 
+// ListOutgoing returns the addressees the caller has already requested (pending or
+// declined) and cannot re-request.
+func (c *Client) ListOutgoing(ctx context.Context, userID string) (OutgoingListResp, error) {
+	var out OutgoingListResp
+	err := c.do(ctx, http.MethodGet, "/api/v1/user/friends/outgoing", userID, "", nil, &out)
+	return out, err
+}
+
 // IssueFriendCode issues a one-time friend code for the caller.
 func (c *Client) IssueFriendCode(ctx context.Context, userID string) (FriendCodeResp, error) {
 	var out FriendCodeResp