tests: cover more exported_private_dependencies cases

[mladedav]

This PR adds tests for all missing cases from #71043 and some on top of that. I believe with this, that issue can be closed.

Some of the lints can be improved, e.g. provided_impl_trait and impl From<PublicWithStdImpl> for OtherType lint twice.

cc @epage in case you want to double check I didn't miss anything.

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[epage]

for symmetry with the struct, should this field be pub?

[mladedav]

Right, fixed.

[mladedav]

This would conflict with #144098 which will most likely break the tests of RPITIT again.

So I'll convert this to a draft so that this doesn't add work there if it's merged first and once that is merged, I'll update this.

It might also mean that the parent issue will still have to be kept open even after mergint this since the current fix in the linked PR breaks linting about using traits from private dependencies again.

[bors]

☔ The latest upstream changes (presumably #144166) made this pull request unmergeable. Please resolve the merge conflicts.

[mladedav]

After #144098, RPITIT is not linted again so that's the last thing that is missing (again). There's a link to a crater run in that PR so if that goes well, that too will be properly linted.

Regardless, this can be merged now and #71043 would just have to wait for the resolution of the crater run and the changes behind that.