rustdoc: default trait methods only show up in search index if they are overridden

initially discovered when searching rustdoc internals for render_into

reproduction code

pub struct Empty;

impl Iterator for Empty {
    type Item = ();

    fn next(&mut self) -> Option<Self::Item> {
        None
    }
}

reproduction steps

1. cargo doc --open --no-deps
2. search for count

expected result

Empty::count shows up as a result, since there is a method callable via that path

actual result

no search results

additional considerations

this could lead to flooding the search results, but hopefully that is no longer an issue once https://github.com/rust-lang/rust/issues/140782 is fixed.

version info

rustdoc 1.86.0 (05f9846f8 2025-03-31)
binary: rustdoc
commit-hash: 05f9846f893b09a1be1fc8560e33fc3c815cfecb
commit-date: 2025-03-31
host: x86_64-unknown-linux-gnu
release: 1.86.0
LLVM version: 19.1.7

Start with the Rust code in the reproduction and run cargo doc --open --no-deps, then search for count in the generated documentation. Trace rustdoc's search-index handling for default trait methods; done means Empty::count appears as a search result even though it is not overridden.