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/game/Game.svelte

@@ -189,6 +189,7 @@
       rackIds = cached.view.rack.map((_, i) => i);
     }
     void load();
+    void loadFriends();
   });
 
   $effect(() => {
@@ -201,6 +202,9 @@
     } else if (e.kind === 'your_turn' && e.gameId === id) void load();
     else if (e.kind === 'chat_message' && e.message.gameId === id && panel === 'chat') void loadChat();
     else if (e.kind === 'nudge' && e.gameId === id && panel === 'chat') void loadChat();
+    // A request the player sent was answered (accepted -> now friends; declined -> stays
+    // "request sent"): re-derive the in-game friend state.
+    else if (e.kind === 'notify' && (e.sub === 'friend_added' || e.sub === 'friend_declined')) void loadFriends();
   });
 
   // Tick the nudge cooldown while the chat is open so the control re-enables on time.
@@ -681,13 +685,31 @@
     }
   }
 
+  // Friend state for the in-game "add to friends" item, derived from the server so it is
+  // correct across reloads and live-updates when a request is answered (Stage 17):
+  // `friends` are the caller's accepted friends; `requested` are the addressees already
+  // requested (pending or declined — both block a re-send and read as "request sent").
+  let friends = $state(new Set<string>());
   let requested = $state(new Set<string>());
   const noop = () => {};
 
+  // loadFriends refreshes the friend/outgoing sets for a non-guest; guests have no social
+  // surfaces, so the sets stay empty. Best-effort — a failure leaves the previous sets.
+  async function loadFriends() {
+    if (app.profile?.isGuest) return;
+    try {
+      const [fl, out] = await Promise.all([gateway.friendsList(), gateway.friendsOutgoing()]);
+      friends = new Set(fl.map((f) => f.accountId));
+      requested = new Set(out.map((f) => f.accountId));
+    } catch {
+      /* best-effort */
+    }
+  }
+
   async function addFriend(accountId: string) {
     try {
       await gateway.friendRequest(accountId);
-      requested = new Set([...requested, accountId]);
+      requested = new Set([...requested, accountId]); // optimistic; reconciled by loadFriends
       showToast(t('friends.requestSent'));
     } catch (e) {
       handleError(e);
@@ -707,9 +729,11 @@
     ...(view?.game.status === 'finished' ? [{ label: t('game.exportGcg'), onclick: exportGcg }] : []),
     ...(!app.profile?.isGuest
       ? opponents.map((s) =>
-          requested.has(s.accountId)
-            ? { label: t('game.requestSent'), onclick: noop, disabled: true }
-            : { label: `${t('friends.addFromGame')}: ${s.displayName}`, onclick: () => addFriend(s.accountId) },
+          friends.has(s.accountId)
+            ? { label: t('game.alreadyFriends'), onclick: noop, disabled: true }
+            : requested.has(s.accountId)
+              ? { label: t('game.requestSent'), onclick: noop, disabled: true }
+              : { label: `${t('friends.addFromGame')}: ${s.displayName}`, onclick: () => addFriend(s.accountId) },
         )
       : []),
     ...(gameOver ? [] : [{ label: t('game.dropGame'), onclick: () => (resignOpen = true) }]),