I believe that everyone is going to be put through the same process that all of us in the Account Migration Beta went through. You can read the beginning of that thread from last year to get an idea.
For now, you don’t need to do a thing. Use ST as you have always been using it. No need to cross over to the new App yet.
When you see the Migration Banner Page magically show up in your current ST Classic app, you will then know you have to cutover. And if you are lucky, maybe ST will send out an email notification ahead of time.