fix(ui): use the guest stubs' "sign in" wording, and link it in Stats

The New Game hint said "Register" where the Stats and Profile guest stubs say
"Sign in". Move the shared word into common.signInLink so the two screens
cannot drift, and turn the Stats stub's opening word into the same link to the
profile screen.

backend/internal/account/link.go

@@ -285,7 +285,7 @@ func (s *Store) AttachIdentity(ctx context.Context, accountID uuid.UUID, kind, e
 // for an already-durable account.
 //
 // The promotion also widens the guest's narrow variant set (GuestVariantPreferences,
-// Эрудит alone) to the registered default, so a player who registers from the New Game
+// Эрудит alone) to the registered default, so a player who signs in from the New Game
 // hint really does gain Russian Scrabble. A guest who changed the set themselves is left
 // alone: only the untouched guest default is replaced.
 func (s *Store) ClearGuest(ctx context.Context, accountID uuid.UUID) error {