clean up and unify logic used by `rustdoc-js` and `rustdoc-js-std` test suites.

[lolbinarycat]

I cannot find the code that actually runs rustdoc on the rustdoc-js/*.rs files, and for some unknown reason, that code is not actually getting run (leading to issues about search-index.js not being found).

This code is quite a mess, rustdoc-js-std seems to be mostly implemented in bootstrap, while rustdoc-js is mostly implemented in compiletest.

This discrepancy leads to an ever increasing number of discrepancies between the exact behavior of the two test suites. Rather than trying to patch these up one by one, I would rather we take a big picture approach.