Test `src\test\rustdoc\macro-document-private-duplicate.rs` fails spuriously

[petrochenkov]

It was a source of failure on CI in PRs like #89144, #88872, #88418, #88530, #88339, #88804 and #82183.
All the failures are on Windows targets, usually MSVC but one is on MinGW as well.

The test was introduced in #88019.

[petrochenkov]

I've disabled the test in 8f035b8 (#88872).

[jyn514]

There isn't a way to fix this without fixing rustdoc; I assume the problem trying to write to the file in two separate threads at the same time causes errors.