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/server/dto.go

@@ -32,12 +32,15 @@ type resolveResponse struct {
 	UserID string `json:"user_id"`
 }
 
-// profileResponse is the authenticated account's own profile.
+// profileResponse is the authenticated account's own profile. AwayStart and AwayEnd
+// are the daily away window's "HH:MM" local-time bounds (in TimeZone).
 type profileResponse struct {
 	UserID              string `json:"user_id"`
 	DisplayName         string `json:"display_name"`
 	PreferredLanguage   string `json:"preferred_language"`
 	TimeZone            string `json:"time_zone"`
+	AwayStart           string `json:"away_start"`
+	AwayEnd             string `json:"away_end"`
 	HintBalance         int    `json:"hint_balance"`
 	BlockChat           bool   `json:"block_chat"`
 	BlockFriendRequests bool   `json:"block_friend_requests"`
@@ -149,6 +152,8 @@ func profileResponseFor(acc account.Account) profileResponse {
 		DisplayName:         acc.DisplayName,
 		PreferredLanguage:   acc.PreferredLanguage,
 		TimeZone:            acc.TimeZone,
+		AwayStart:           acc.AwayStart.Format(awayTimeLayout),
+		AwayEnd:             acc.AwayEnd.Format(awayTimeLayout),
 		HintBalance:         acc.HintBalance,
 		BlockChat:           acc.BlockChat,
 		BlockFriendRequests: acc.BlockFriendRequests,
@@ -156,6 +161,9 @@ func profileResponseFor(acc account.Account) profileResponse {
 	}
 }
 
+// awayTimeLayout is the "HH:MM" wire form of the daily away-window bounds.
+const awayTimeLayout = "15:04"
+
 // gameDTOFromGame projects a game.Game into its DTO.
 func gameDTOFromGame(g game.Game) gameDTO {
 	seats := make([]seatDTO, 0, len(g.Seats))