"downstream crates may implement trait for type" for both trait and type private to this crate

$ rustc --version
rustc 1.83.0-nightly (363ae4188 2024-09-24)

use std::cmp::Ordering;
use compare::Compare;
use num_cmp::NumCmp;

trait PartialCompare<L: ?Sized, R: ?Sized = L> {
    fn compare(&self, l: &L, r: &R) -> Option<Ordering>;
}

impl<L, R, C: Compare<L, R>> PartialCompare<L, R> for C {
    fn compare(&self, l: &L, r: &R) -> Option<Ordering> {
        Some(self.compare(l, r))
    }
}

#[derive(Default, Debug, Clone, Copy)]
struct NumCompare;

impl<L, R> PartialCompare<L, R> for NumCompare
where
    L: NumCmp<R> + Copy,
    R: Copy,
{
    fn compare(&self, l: &L, r: &R) -> Option<Ordering> {
        NumCmp::num_cmp(*l, *r)
    }
}


fn main() {}

With dependencies:

num-cmp = "0.1.0"
compare = "0.1.0"

Failed to compile:

error[E0119]: conflicting implementations of trait `PartialCompare<_, _>` for type `NumCompare`
  --> src/main.rs:18:1
   |
9  |   impl<L, R, C: Compare<L, R>> PartialCompare<L, R> for C {
   |   ------------------------------------------------------- first implementation here
...
18 | / impl<L, R> PartialCompare<L, R> for NumCompare
19 | | where
20 | |     L: NumCmp<R> + Copy,
21 | |     R: Copy,
   | |____________^ conflicting implementation for `NumCompare`
   |
   = note: downstream crates may implement trait `compare::Compare<_, _>` for type `NumCompare`

Since both PartialCompare and NumCompare are defined in this crate, the error message seems incorrect. Not sure it's a bug or an error messaging inaccurate.

Start by compiling the supplied Rust example with the reported rustc 1.83.0-nightly version and confirm the E0119 diagnostic. Trace the coherence-checking diagnostic path and its handling of private traits and types; done means the diagnostic accurately describes whether a downstream implementation can create the conflict, with regression coverage for this example.