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/account/timezone.go

@@ -0,0 +1,56 @@
+package account
+
+import (
+	"regexp"
+	"strconv"
+	"time"
+)
+
+// offsetZoneRe matches a fixed UTC offset like "+03:00" or "-05:30" — the form the
+// Stage 8 profile editor stores (an offset dropdown rather than an IANA name).
+var offsetZoneRe = regexp.MustCompile(`^([+-])(\d{2}):(\d{2})$`)
+
+// parseOffsetZone parses a "±HH:MM" offset into a fixed-offset location, reporting
+// ok=false when name is not a well-formed offset within ±14:00.
+func parseOffsetZone(name string) (*time.Location, bool) {
+	m := offsetZoneRe.FindStringSubmatch(name)
+	if m == nil {
+		return nil, false
+	}
+	h, _ := strconv.Atoi(m[2])
+	min, _ := strconv.Atoi(m[3])
+	if h > 14 || min > 59 || (h == 14 && min > 0) {
+		return nil, false
+	}
+	secs := h*3600 + min*60
+	if m[1] == "-" {
+		secs = -secs
+	}
+	return time.FixedZone(name, secs), true
+}
+
+// ResolveZone resolves a stored timezone — a fixed "±HH:MM" offset or an IANA name —
+// to a *time.Location, falling back to UTC when it is empty or unrecognised, so a
+// bad profile value never breaks the turn-timeout sweeper or the robot's sleep.
+func ResolveZone(name string) *time.Location {
+	if name == "" {
+		return time.UTC
+	}
+	if loc, ok := parseOffsetZone(name); ok {
+		return loc
+	}
+	if loc, err := time.LoadLocation(name); err == nil {
+		return loc
+	}
+	return time.UTC
+}
+
+// validZone reports whether name is an acceptable timezone for a profile update —
+// either a "±HH:MM" offset or a loadable IANA location.
+func validZone(name string) bool {
+	if _, ok := parseOffsetZone(name); ok {
+		return true
+	}
+	_, err := time.LoadLocation(name)
+	return err == nil
+}