Check hidden/private items documentation in `rustdoc`

Checking hidden/private items in rustdoc can be useful even if no docs are generated/displayed for them. For instance to detect broken intra-doc links there: someone may try to link something that didn't exist, for instance because there was a typo, or the docs became outdated, etc.

It is also nice when something is made public or un-hidden, or when the docs are copy-pasted to somewhere else, i.e. they would have a higher chance of working. Put another way, not checking means that the hidden/private items are, in a sense, less strict.

The fact that they are not checked can be surprising on its own. For instance, there was a brief period of time in 1.92's nightlies when checking actually took place by mistake [1][2], which made @BennoLossin send a fix for it, wondering why previous versions didn't catch it [3].

This can be worked around by doing two passes (i.e. one for checking, and one for the actual generation) with the --document-{hidden,private}-items flags (suggested by Guillaume). However, that requires two passes where one (the bigger one, in fact) will be simply discarded.

A related feature that can cover this one for some projects is the "Runtime toggle for private/hidden items documentation (and /* private fields */)" one, i.e. if there was a runtime toggle to see the private/hidden items, then the docs for those would of course have been checked already even if most users do not see/read them. That feature on its own is something that would be quite interesting [4].

[1] https://github.com/rust-lang/rust/pull/147153#issuecomment-3395484636
[2] https://github.com/rust-lang/rust/pull/147809
[3] https://lore.kernel.org/all/20251016211740.653599-1-lossin@kernel.org/T/
[4] https://github.com/rust-lang/rust/issues/149106

Cc @GuillaumeGomez @fmease @lolbinarycat

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

Start with rustdoc's handling of the --document-hidden-items and --document-private-items flags, then read the linked issue #149106 and the referenced pull requests for prior behavior. Determine how intra-doc links in hidden and private items can be checked without a second discarded documentation pass; done means those links are validated while normal documentation output remains unchanged.