Stage 8 polish: profile validation, finished-game UI, badge + Safari fixes

Owner-review follow-up on the Stage 8 branch:
- Friend code is copyable (📋 + toast). The lobby notification badge is fixed —
  it had inherited the hamburger-bar style — into a proper round count dot.
- Safari: min-width:0 on flex text inputs (friend code, profile, chat) so they
  shrink instead of pushing the adjacent button off-screen.
- Profile editing is validated on both the UI and the backend: display-name format
  (letters joined by single space/./_ separators, no leading/trailing/adjacent
  separators, <=32 runes), a UTC-offset timezone picker (account.ResolveZone parses
  ±HH:MM or a legacy IANA name), a 10-minute away grid capped at 12h (wrap-aware),
  and email format; Save is disabled and invalid fields red-bordered until valid.
  Language stays in Settings.
- In a game, an "add to friends" menu item flips to a disabled "request sent"; chat
  send/nudge became ⬆️/🛎️ icon buttons.
- A finished game drops its last-word highlight, hides Check word / Drop game,
  disables zoom, and draws an inert (greyed) footer instead of hiding it.

Tests: account validators (name/away/zone), UI profileValidation, e2e for the
finished-game footer/menu and the copy control. Docs (PLAN, ARCHITECTURE,
FUNCTIONAL +ru, UI_DESIGN) updated for the display-name rule, UTC-offset timezone
and the 12h away window.

backend/internal/game/timeout.go

@@ -5,6 +5,8 @@ import (
 	"time"
 
 	"go.uber.org/zap"
+
+	"scrabble/backend/internal/account"
 )
 
 // effectiveDeadline is the instant a turn auto-resigns. It is the raw deadline
@@ -57,17 +59,11 @@ func minutesOfDay(t time.Time) int {
 	return t.Hour()*60 + t.Minute()
 }
 
-// loadLocation resolves an IANA timezone name, falling back to UTC when it is
-// empty or unknown (so a bad profile value never breaks the sweeper).
+// loadLocation resolves a stored timezone (an IANA name or a "±HH:MM" offset),
+// falling back to UTC when it is empty or unknown (so a bad profile value never
+// breaks the sweeper). It defers to account.ResolveZone, the single source of truth.
 func loadLocation(name string) *time.Location {
-	if name == "" {
-		return time.UTC
-	}
-	loc, err := time.LoadLocation(name)
-	if err != nil {
-		return time.UTC
-	}
-	return loc
+	return account.ResolveZone(name)
 }
 
 // SweepTimeouts auto-resigns every active game whose current turn has exceeded