rustdoc search in `std` for complex signature is significantly slower

[cyrgani]

Using the suggested example search Option<T>, (T -> U) -> Option<U> on nightly std docs (link) now takes around 20 seconds to finish for me.
Trying this out on stable still finishes much faster, in around one second (link).
Likely because of #144476.

[fmease]

cc @notriddle