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/encode_social.go

@@ -54,6 +54,16 @@ func encodeIncomingList(r backendclient.IncomingListResp) []byte {
 	return b.FinishedBytes()
 }
 
+// encodeOutgoingList builds an OutgoingRequestList payload.
+func encodeOutgoingList(r backendclient.OutgoingListResp) []byte {
+	b := flatbuffers.NewBuilder(256)
+	v := buildAccountRefVector(b, r.Requests, fb.OutgoingRequestListStartRequestsVector)
+	fb.OutgoingRequestListStart(b)
+	fb.OutgoingRequestListAddRequests(b, v)
+	b.Finish(fb.OutgoingRequestListEnd(b))
+	return b.FinishedBytes()
+}
+
 // encodeBlockList builds a BlockList payload.
 func encodeBlockList(r backendclient.BlockListResp) []byte {
 	b := flatbuffers.NewBuilder(256)