Detect need for partial `self` borrows in methods and suggest alternatives

When encountering methods where getters on self are used which cause borrow errors like the following:

error[E0502]: cannot borrow `*self` as mutable because it is also borrowed as immutable
  --> src/lib.rs:20:17
   |
19 |         let a = self.get_a();
   |                 ---- immutable borrow occurs here
20 |         let b = self.get_mut_b();
   |                 ^^^^^^^^^^^^^^^^ mutable borrow occurs here
21 |         println!("{a:?} {b:?}");
   |                    - immutable borrow later used here

error[E0502]: cannot borrow `self.b` as mutable because it is also borrowed as immutable
  --> src/lib.rs:29:9
   |
29 |         self.b.bar(self.get_a());
   |         ^^^^^^^---^----^^^^^^^^^
   |         |      |   |
   |         |      |   immutable borrow occurs here
   |         |      immutable borrow later used by call
   |         mutable borrow occurs here

error[E0502]: cannot borrow `*self` as mutable because it is also borrowed as immutable
  --> src/lib.rs:35:9
   |
35 |         self.bar(self.get_a());
   |         ^^^^^---^----^^^^^^^^^
   |         |    |   |
   |         |    |   immutable borrow occurs here
   |         |    immutable borrow later used by call
   |         mutable borrow occurs here

error[E0502]: cannot borrow `*self` as mutable because it is also borrowed as immutable
  --> src/lib.rs:37:9
   |
37 |         self.bar(&self.a);
   |         ^^^^^---^-------^
   |         |    |   |
   |         |    |   immutable borrow occurs here
   |         |    immutable borrow later used by call
   |         mutable borrow occurs here

we should explain that get_a and get_mut_b borrow the entirety of Self making accessing any other method or field simultaneously will never work. If we ever get partial self borrows, then we should suggest it here.

Start with the linked Rust Playground reproducer and the E0502 diagnostics shown in the issue. Trace where these borrow errors are diagnosed and determine how the diagnostic should explain whole-self borrows; done means the current examples receive that explanation and partial-self-borrow support produces an appropriate suggestion.