Regression in error reporting on {integer} type ambiguity between 1.61 and 1.62

[mqudsi]

This is strongly related to #98357.

The presence of a Mul impl for both u8 and i32 introduces an ambiguity in main() where the type of the literal 7 cannot be determined. #98357 goes into why this is an error since it can be fixed by assigning a type (Foo) to prod, but this issue is about a regression in rustc 1.62 which drops information about the ambiguity in the literal integer's type from the error message/notes as compared to 1.61 (which does not).

use core::ops::Mul;

#[derive(Debug)]
struct Foo(i32);

impl Mul<Foo> for i32 {
    type Output = Foo;

    fn mul(self, other: Foo) -> Self::Output {
        Foo(self * other.0)
    }
}

impl Mul<Foo> for u8 {
    type Output = Foo;
    
    fn mul(self, other: Foo) -> Self::Output {
        Foo(self as i32 * other.0)
    }
}

fn main() {
    let prod = 7 * Foo(6);
    assert_eq!(prod.0, 42);
}

Playground link

The error message emitted by 1.61 (current stable):

error[[E0282]](https://doc.rust-lang.org/stable/error-index.html#E0282): type annotations needed
  --> src/main.rs:24:16
   |
23 |     let prod = 7 * Foo(6);
   |         ---- consider giving `prod` a type
24 |     assert_eq!(prod.0, 42);
   |                ^^^^ cannot infer type
   |
   = note: type must be known at this point

error[[E0283]](https://doc.rust-lang.org/stable/error-index.html#E0283): type annotations needed
  --> src/main.rs:23:18
   |
23 |     let prod = 7 * Foo(6);
   |                  ^ cannot infer type for type `{integer}`
   |
note: multiple `impl`s satisfying `{integer}: Mul<Foo>` found
  --> src/main.rs:6:1
   |
6  | impl Mul<Foo> for i32 {
   | ^^^^^^^^^^^^^^^^^^^^^
...
14 | impl Mul<Foo> for u8 {
   | ^^^^^^^^^^^^^^^^^^^^

Some errors have detailed explanations: E0282, E0283.
For more information about an error, try `rustc --explain E0282`.

The error message emitted by 1.62 (2022-06-13 1bc802e) (the current beta):

error[[E0282]](https://doc.rust-lang.org/beta/error-index.html#E0282): type annotations needed
  --> src/main.rs:24:16
   |
23 |     let prod = 7 * Foo(6);
   |         ---- consider giving `prod` a type
24 |     assert_eq!(prod.0, 42);
   |                ^^^^ cannot infer type
   |
   = note: type must be known at this point

For more information about this error, try `rustc --explain E0282`.

Notice that while one perhaps valid resolution has been provided, the actual cause of the error is completely obscured.

[apiraino]

WG-prioritization assigning priority (Zulip discussion).

@rustbot label -I-prioritize +P-medium

[mqudsi]

@rustbot label +A-diagnostics