[clang-tools-extra] [clang-tidy] Fix result check after overwriteChangedFiles() (PR #86360)

[Piotr Zegar via cfe-commits]

https://github.com/PiotrZSL approved this pull request.

LGTM.
Yes looks like previously AnyNotWritten coudn't be `true`.

I don't see need for test / release notes.
After all the only thing this impact is a print.

https://github.com/llvm/llvm-project/pull/86360