Rollup merge of #47250 - GuillaumeGomez:test-rustdoc-js, r=Mark-Simulacrum

Test rustdoc js

Add tests for the rustdoc search. It was heavily required because of all the recent breaking changes that happened while I went through improvements in doc search (add search in/for generic search for example).

diff --cc src/bootstrap/builder.rs
Simple merge

diff --cc src/bootstrap/check.rs
Simple merge

diff --cc src/bootstrap/doc.rs
Simple merge