`private_interfaces` lint needs to perform type resolution to avoid false positives

The private_interfaces lint incorrectly fires for cases where a type is declared via a private interface but nevertheless fully resolves to an equally (or more) public type.

trait Service {
    type Output;
    
    fn process() -> Self::Output;
}

pub struct SomeService;
impl Service for SomeService {
    type Output = ();
    
    fn process() -> Self::Output {
        todo!();
    }
}

// False positive on return type here:
pub fn exposed_method() -> <SomeService as Service>::Output {
    SomeService::process()
}

Currently produces the following error on both 1.91.1 stable and 1.93.0-nightly:

warning: associated type `Service::Output` is more private than the item `exposed_method`
  --> src/lib.rs:16:1
   |
16 | pub fn exposed_method() -> <SomeService as Service>::Output {
   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ function `exposed_method` is reachable at visibility `pub`
   |
note: but associated type `Service::Output` is only usable at visibility `pub(crate)`
  --> src/lib.rs:2:5
   |
 2 |     type Output;
   |     ^^^^^^^^^^^
   = note: `#[warn(private_interfaces)]` on by default

warning: trait `Service` is more private than the item `exposed_method`
  --> src/lib.rs:16:1
   |
16 | pub fn exposed_method() -> <SomeService as Service>::Output {
   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ function `exposed_method` is reachable at visibility `pub`
   |
note: but trait `Service` is only usable at visibility `pub(crate)`
  --> src/lib.rs:1:1
   |
 1 | trait Service {
   | ^^^^^^^^^^^^^

Playground link: https://play.rust-lang.org/?version=nightly&mode=debug&edition=2024&gist=4756e3d350f5f0bdd90086f76d043a89

As you can see, the private_interfaces lint is automatically fired when a less-public type is encountered in the type signature, but if type resolution were performed it would be obvious that this actually resolves to a very much public and accessible type (in this case, ()).

(This is a very much contrived example; in my actual code I have a trait that exposes blocking methods via a non-blocking async interface and the trait's associated type is the shortest and least error-prone method of expressing the type of a pub static)

@rustbot label +T-compiler +L-private_interfaces +L-false-positive +A-visibility +A-lints +C-bug

Reproduce the false positive from the linked Rust Playground example, then trace the compiler's private_interfaces lint and its type-resolution handling. The work is done when the shown () return type no longer triggers warnings for the private trait or associated type, with regression coverage for the example.