How might I manage my anxiety that I will miss something important if I disconnect entirely? It keeps me doing things like leaving my phone outside of my bedroom overnight.

Make sure that your phone isn’t the only place you put things in. Have a agenda with you at all times, to use it right when you get told something that will need to be done at a certain time, have a pencil/pen and a notebook or agenda ready at that time. And before you disconnect check your agenda and make sure that you’re not missing anything important.