If you're using a single threaded reactor you don't need a mutex at all; a Rc<RefCell<_>> will do just fine. And if you want other tasks to yield until you're done holding the borrow, the solution is simple: don't await until you're done.
https://docs.rs/tokio/latest/tokio/task/struct.LocalSet.html...there are absolutely situations where tokio's mutex and rwlock are useful, but the vast majority of the time you shouldn't need them