Unhelpful diagnostic when infered lifetime of return value doesn't match parameter in closure

[lukas-code]

Given the following code: Playground

fn find_by_key<T, K>(_get_key: impl FnMut(&T) -> K) {
    
}

fn get_key((key, _) : &(String, u8)) -> &str {
    key
}
    
fn main() {
    find_by_key(get_key);
}

The current output is:

Compiling playground v0.0.1 (/playground)
error[[E0308]](https://doc.rust-lang.org/stable/error-index.html#E0308): mismatched types
  --> src/main.rs:10:5
   |
10 |     find_by_key(get_key);
   |     ^^^^^^^^^^^^^^^^^^^^ one type is more general than the other
   |
   = note: expected trait `for<'r> <for<'r> fn(&'r (String, u8)) -> &'r str {get_key} as FnOnce<(&'r (String, u8),)>>`
              found trait `for<'r> <for<'r> fn(&'r (String, u8)) -> &'r str {get_key} as FnOnce<(&'r (String, u8),)>>`
note: the lifetime requirement is introduced here
  --> src/main.rs:1:50
   |
1  | fn find_by_key<T, K>(_get_key: impl FnMut(&T) -> K) {
   |                                                  ^

For more information about this error, try `rustc --explain E0308`.
error: could not compile `playground` due to previous error

This diagnostic shows the lifetimes of the function item, but omits the return lifetime on the function trait.
(It also shows the wrong fn trait.)

Ideally the output should only show the lifetimes on the fn traits and suggest restricting the lifetime of the parameter:

Compiling playground v0.0.1 (/playground)
error[[E0308]](https://doc.rust-lang.org/stable/error-index.html#E0308): mismatched types
  --> src/main.rs:10:5
   |
10 |     find_by_key(get_key);
   |     ^^^^^^^^^^^^^^^^^^^^ one type is more general than the other
   |
   = note: expected trait `for<'a, 'r> FnMut(&'r (String, u8)) -> &'a str`
              found trait `for<'r> FnMut(&'r (String, u8)) -> &'r str`
note: the lifetime requirement `'a` is introduced here
  --> src/main.rs:1:50
   |
1  | fn find_by_key<T, K>(_get_key: impl FnMut(&T) -> K) {
   |                                                  ^
help: Try restricting the lifetime of the argument to `'a`:
   |
1  | fn find_by_key<'a, T: 'a, K>(_get_key: impl FnMut(&'a T) -> K) {
   |                ++   ++++                           ++

For more information about this error, try `rustc --explain E0308`.
error: could not compile `playground` due to previous error

[lukas-code]

@rustbot label +A-lifetimes +D-confusing +D-terse

[lukas-code]

triage: closing this in favor of #112985.