Rollup merge of #145650 - GuillaumeGomez:fix-js-search-scripts-path, r=fmease

Fix JS search scripts path

`rootPath` always end with a `/` so we should not add one. Interestingly enough, it only triggers the bug on a website (like https://doc.rust-lang.org/nightly/std/).

Follow-up of rust-lang/rust#144476.
Fixes rust-lang/rust#145646.

cc `````@notriddle`````
r? `````@fmease`````

Author: jhpratt