Rollup merge of #128578 - camelid:cache-index-cleanup, r=notriddle

rustdoc: Cleanup `CacheBuilder` code for building search index

This code was very convoluted and hard to reason about. It is now (I hope) much
clearer and more suitable for both future enhancements and future cleanups.

I'm doing this as a precursor, with no UI changes, to changing rustdoc to
[ignore blanket impls][1] in type-based search.

[1]: rust-lang/rust#128471 (comment)

r? ``@notriddle``