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/e2e/smoke.spec.ts

@@ -8,7 +8,7 @@ test('guest reaches a board and previews a placement', async ({ page }) => {
 
   await page.getByRole('button', { name: /guest/i }).click();
 
-  await expect(page.getByText('Active games')).toBeVisible();
+  await expect(page.getByText('Your turn')).toBeVisible();
   const activeRow = page.getByRole('button', { name: /Ann/ });
   await expect(activeRow).toBeVisible();
   await activeRow.click();

ui/e2e/social.spec.ts

@@ -7,7 +7,7 @@ import { expect, test, type Page } from './fixtures';
 async function loginLobby(page: Page): Promise<void> {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await expect(page.getByText('Active games')).toBeVisible();
+  await expect(page.getByText('Your turn')).toBeVisible();
 }
 
 async function openFriends(page: Page): Promise<void> {
@@ -107,7 +107,7 @@ test('play with friends: a game type is required to send an invitation', async (
   await expect(send).toBeEnabled();
 
   await send.click(); // the mock creates it and returns to the lobby
-  await expect(page.getByText('Active games')).toBeVisible();
+  await expect(page.getByText('Your turn')).toBeVisible();
 });
 
 test('game: add-to-friends flips to a disabled "request sent"', async ({ page }) => {

ui/e2e/telegram.spec.ts

@@ -27,7 +27,7 @@ test('Telegram launch auto-authenticates into the lobby and applies the theme',
   await page.goto('/');
 
   // No guest-login click: the Mini App authenticates from initData and lands on the lobby.
-  await expect(page.getByText('Active games')).toBeVisible();
+  await expect(page.getByText('Your turn')).toBeVisible();
 
   // The Telegram themeParams override the background token at runtime.
   await expect