1. Wherever the `buf` field of a `Formatter` was used, the `Formatter` is used
instead.
2. The usage of `write_fmt` is minimized as much as possible, the `write!` macro
is preferred wherever possible.
3. Usage of `fmt::write` is minimized, favoring the `write!` macro instead.
If you were writing to something along the lines of `self.foo` then with the new
closure rules it meant that you were borrowing `self` for the entirety of the
closure, meaning that you couldn't format other fields of `self` at the same
time as writing to a buffer contained in `self`.
By lifting the borrow outside of the closure the borrow checker can better
understand that you're only borrowing one of the fields at a time. This had to
use type ascription as well in order to preserve trait object coercions.