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.

docs/FUNCTIONAL.md

@@ -58,7 +58,11 @@ account is kept and the guest's games move into it. A merge is blocked only whil
 two accounts share a game still in progress.
 
 ### Lobby & matchmaking *(Stage 4 / 15)*
-Bottom tab menu: **my games**, **profile**. The game types offered on **New Game** are
+Bottom tab menu: **my games**, **profile**. The **my games** list groups games into three
+sections — *your turn*, *opponent's turn* and *finished* (empty sections are hidden) — and
+orders them so the games awaiting your move come first, the longest-waiting on top, while
+opponent-turn and finished games are most-recent first; it renders as a compact,
+line-separated list (Stage 17). The game types offered on **New Game** are
 limited to the languages the player's sign-in service supports (English → Scrabble;
 Russian → Scrabble + Erudite; a bilingual service shows all three, and the web client is
 unrestricted). Variants are shown by their **display name** — both Scrabble variants read
@@ -111,7 +115,10 @@ digits, valid for twelve hours), or send a **request to someone you have played
 with** — they accept, ignore it (a request lapses after thirty days and can then be
 re-sent), or decline (a decline blocks further requests from you until they hand you
 a code). Cancelling your own pending request withdraws it; unfriending removes the
-friendship. Block globally — switch off incoming chat
+friendship. In a game, an **add to friends** item for each opponent mirrors the live
+relationship: it reads *request sent* (disabled) while a request is pending or was
+declined, and *in friends* once accepted — updating in place the moment the opponent
+answers, and staying correct across reloads (Stage 17). Block globally — switch off incoming chat
 and/or friend requests — and block individual players (a per-user block hides that
 person's chat and stops requests and game invitations both ways; it also ends any
 existing friendship). Per-game chat is for quick reactions: messages are short