Stage 8: UI social/account/history surfaces

Wire the deferred Stage 7 surfaces end-to-end (UI -> gateway transcode ->
backend REST -> existing domain services): friends (incl. one-time friend
codes), per-user blocks, friend-game invitations, profile editing + email
binding, the statistics screen, and the in-game history + GCG export.

Friends gain two add paths (interview decision, a deliberate plan change):
one-time 6-digit codes (friend_codes table, 12h TTL, single-use, rate-limited
redeem); and play-gated requests (shared game required) where an explicit
decline is permanent, an ignored request lapses after 30 days, and a code
bypasses a decline. Migration 00006 widens friendships_status_chk and adds
friend_codes.

Lobby notification badge is poll + push: a new generic `notify` event drives
it live; the client polls on open/focus. Language stays a single Settings
control that writes through to the durable account's preferred_language. GCG
export is finished-only (game.ErrGameActive) and shares/downloads the .gcg file.

Tests: backend unit + inttest (friend gate/decline/code, ListInvitations,
GetStats, GCG gate), gateway transcode round-trips + notify constructor, UI
vitest (codecs, win-rate, share choice) + Playwright social specs. Docs: PLAN
(Stage 8 done + refinements + TODO-5), ARCHITECTURE, FUNCTIONAL(+ru), UI_DESIGN,
TESTING, module READMEs.

ui/src/lib/stats.test.ts

@@ -0,0 +1,26 @@
+import { describe, expect, it } from 'vitest';
+import { gamesPlayed, winRate } from './stats';
+import type { Stats } from './model';
+
+const s = (wins: number, losses: number, draws: number): Stats => ({
+  wins,
+  losses,
+  draws,
+  maxGamePoints: 0,
+  maxWordPoints: 0,
+});
+
+describe('stats', () => {
+  it('sums games played', () => {
+    expect(gamesPlayed(s(7, 4, 1))).toBe(12);
+  });
+
+  it('computes a rounded win rate', () => {
+    expect(winRate(s(7, 4, 1))).toBe(58); // 7/12 = 58.33 -> 58
+    expect(winRate(s(1, 1, 0))).toBe(50);
+  });
+
+  it('win rate is 0 with no games', () => {
+    expect(winRate(s(0, 0, 0))).toBe(0);
+  });
+});