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/inttest/social_test.go

@@ -84,7 +84,7 @@ func TestFriendRequestRefusedByToggleAndBlock(t *testing.T) {
 
 	// Toggle: the addressee does not accept friend requests.
 	a, b := provisionAccount(t), provisionAccount(t)
-	if _, err := store.UpdateProfile(ctx, b, account.ProfileUpdate{PreferredLanguage: "en", TimeZone: "UTC", BlockFriendRequests: true}); err != nil {
+	if _, err := store.UpdateProfile(ctx, b, account.ProfileUpdate{DisplayName: "Player", PreferredLanguage: "en", TimeZone: "UTC", BlockFriendRequests: true}); err != nil {
 		t.Fatalf("set toggle: %v", err)
 	}
 	if err := svc.SendFriendRequest(ctx, a, b); !errors.Is(err, social.ErrRequestBlocked) {
@@ -257,7 +257,7 @@ func TestChatPostListAndBlocks(t *testing.T) {
 	if _, err := svc.PostMessage(ctx, other, seats2[0], "hi", ""); err != nil {
 		t.Fatalf("post 2: %v", err)
 	}
-	if _, err := store.UpdateProfile(ctx, seats2[1], account.ProfileUpdate{PreferredLanguage: "en", TimeZone: "UTC", BlockChat: true}); err != nil {
+	if _, err := store.UpdateProfile(ctx, seats2[1], account.ProfileUpdate{DisplayName: "Player", PreferredLanguage: "en", TimeZone: "UTC", BlockChat: true}); err != nil {
 		t.Fatalf("set block_chat: %v", err)
 	}
 	if msgs, _ := svc.Messages(ctx, other, seats2[1]); len(msgs) != 0 {