Describe the problem you are trying to solve

#7593 enables --document-private-items flag by default for binary crates. As stated in the PR:

We should also probably add a --document-only-public-items flag or something like that if we change the default behavior. Otherwise users have no way to not document private items for binary crates. Right? -> We can do it later

Describe the solution you'd like

Add flag like --document-only-public-items which can be used for binary crates to disable flag --document-private-items (which is enabled by default)