Runtime toggle for private/hidden items documentation

[ojeda]

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 #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.

#141299

Cc @GuillaumeGomez @fmease @lolbinarycat

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