rustbuild: `doc-rustc` overwrites search index

[TimNN]

Building the compiler docs with rustbuild overwrites the js search index of the std docs with the one from the compiler docs.

Example: https://rust-beta-doc.timnn.me/std/index.html?search=String (that is no longer live).

[alexcrichton]

Hm I think that this may be a result of a little too aggressively cleaning out the doc directory, there's probably some fs::remove_dir_all which should be sequenced differently or perhaps just not run at all.

[ollie27]

This was fixed by #40199.

[alexcrichton]

Indeed!