Runtime toggle for private/hidden items documentation

In some projects, it can be useful to see private/hidden items/documentation/details (and /* private fields */ etc.) without having to go into the source view, which isn't as nice.

Instead of re-rendering the documentation with --document-private-items and --document-hidden-items, it would be very interesting to have a runtime toggle (i.e. in the web UI) that users could click to show hidden and/or private items on the fly.

This feature would also mean that we would already get checking for private/hidden items, i.e. it could be an alternative for https://github.com/rust-lang/rust/issues/149105 for those that want to use the runtime toggle anyway.

This can be worked around on the user side by generating every documentation set needed and then adding custom UI. Of course, that is slower, takes more space, doesn't allow for an implementation that avoids reloading, users need to reimplement the same idea, etc.

https://github.com/rust-lang/rust/pull/141299

Cc @GuillaumeGomez @fmease @lolbinarycat

@rustbot label T-rustdoc
@rustbot label A-intra-doc-links
@rustbot label A-rust-for-linux

Start by reviewing the existing --document-private-items and --document-hidden-items behavior and the linked PR #141299. Then examine the rustdoc web UI approach described in the issue. Done means users can toggle private and hidden items at runtime without regenerating or reloading the documentation, while retaining the relevant checking behavior.