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.

backend/internal/inttest/lobby_test.go

@@ -165,3 +165,31 @@ func TestInvitationCancelByInviter(t *testing.T) {
 		t.Fatalf("respond after cancel = %v, want ErrInvitationNotPending", err)
 	}
 }
+
+func TestListInvitations(t *testing.T) {
+	ctx := context.Background()
+	svc := newInvitationService()
+	inviter := provisionAccount(t)
+	invitee := provisionAccount(t)
+	inv, err := svc.CreateInvitation(ctx, inviter, []uuid.UUID{invitee}, englishInvite())
+	if err != nil {
+		t.Fatalf("create: %v", err)
+	}
+	// An open invitation appears for both the inviter and the invitee.
+	for _, who := range []uuid.UUID{inviter, invitee} {
+		list, err := svc.ListInvitations(ctx, who)
+		if err != nil {
+			t.Fatalf("list for %s: %v", who, err)
+		}
+		if len(list) != 1 || list[0].ID != inv.ID {
+			t.Fatalf("invitations for %s = %+v, want [%s]", who, list, inv.ID)
+		}
+	}
+	// Once accepted (the game starts), it is no longer an open invitation.
+	if _, err := svc.RespondInvitation(ctx, inv.ID, invitee, true); err != nil {
+		t.Fatalf("accept: %v", err)
+	}
+	if list, _ := svc.ListInvitations(ctx, inviter); len(list) != 0 {
+		t.Fatalf("started invitation still listed: %+v", list)
+	}
+}