`--emit obj` with `--crate-type staticlib` doesn't work when `-C lto=thin` is set

I tried this code:

// answer.rs
pub fn answer() -> u64 {
    42
}

And compiled it with:

rustc answer.rs --crate-type staticlib --emit obj -C lto=thin

I expected to see an object file created. Instead it appears to succeed but no object file is produced.

Meta

rustc --version --verbose:

rustc 1.82.0 (f6e511eec 2024-10-15)
binary: rustc
commit-hash: f6e511eec7342f59a25f7c0534f1dbea00d01b14
commit-date: 2024-10-15
host: x86_64-pc-windows-msvc
release: 1.82.0
LLVM version: 19.1.1

Reproduce the issue with answer.rs and the reported rustc command using --crate-type staticlib, --emit obj, and -C lto=thin. Trace rustc's handling of these options and compare the output behavior with the expectation that an object file is created. Done means the command produces the expected object file and has coverage for this combination.