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/notify/notify.go

@@ -24,6 +24,18 @@ const (
 	KindChatMessage   = "chat_message"
 	KindNudge         = "nudge"
 	KindMatchFound    = "match_found"
+	// KindNotification is a lightweight "re-poll your lobby counters" signal
+	// (incoming friend requests, invitations) that drives the lobby badge.
+	KindNotification = "notify"
+)
+
+// Notification sub-kinds carried in a KindNotification event payload; the client
+// re-fetches its lobby counters on any of them.
+const (
+	NotifyFriendRequest = "friend_request"
+	NotifyFriendAdded   = "friend_added"
+	NotifyInvitation    = "invitation"
+	NotifyGameStarted   = "game_started"
 )
 
 // Intent is one live event destined for a single user. Payload is the