False Positive: `needless_raw_string_hashes` when combined with `const_format::formatcp`

Summary

When using formatcp! from const_format,
Some FPs happen, following (to me) strange rules.
The same does not happen using the same string in e.g. println!.

Lint Name

needless_raw_string_hashes

Reproducer

Using const_format = "0.2" in Cargo.toml.

I tried this code:

#![deny(clippy::needless_raw_string_hashes)]

use const_format::formatcp;

const C: &str = "c";

fn main() {
    println!(
        "{}",
        formatcp!(
            // NOTE warning -> false positive!
            r#"a "b" {C} d"#
        )
    );

    println!(
        "{}",
        formatcp!(
            // no warning -> correct
            r#"a "b" {C}"#
        )
    );
}

I saw this happen:

error: unnecessary hashes around raw string literal
  --> clippy-raw-string-lit-test/src/main.rs:15:13
   |
15 |             r#"a "b" {C} d"#
   |             ^^^^^^^^^^^^^^^^

I expected to see this happen:

Version

rustc 1.75.0-nightly (9d83ac217 2023-10-31)
binary: rustc
commit-hash: 9d83ac217957eece2189eccf4a7232caec7232ee
commit-date: 2023-10-31
host: x86_64-unknown-linux-gnu
release: 1.75.0-nightly
LLVM version: 17.0.3

Additional Labels

No response

Start by reproducing the false positive from the issue in clippy-raw-string-lit-test/src/main.rs, using the provided const_format::formatcp examples. Compare the two raw string cases and trace the needless_raw_string_hashes lint handling. Done means the first case no longer produces a false positive while the lint continues to report genuinely unnecessary hashes.