I recently moved my wife to a new phone. It took only a couple of minutes to transfer the esim. But SMS was blocked for 24 hours. Some kind of security measure? So I couldn't activate any apps that required 2FA via SMS. Quite a hassle.
eSIM is a failed technology. Instead of making it easier to move, they just gave the operators more control. In some cases, transfers are simply not possible (like with most eSIMs on Airalo)