How likely is it an agency would request to review performance records during hiring?

I had an unsatisfactory performance review this year right as I am preparing to leave my current agency but would like to stay in state service. Some of it is valid-- I did not intentionally or maliciously mess things up, but due to a bunch of misunderstandings of procedure, and vague responses from my supervisor when I attempted to clarify things, I made some pretty big screw-ups, and I accept that those will have consequences. But other things in there that my supervisor called performance deficits that continued despite coaching were not actually raised with me as issues and I did not receive meaningful coaching on them. (Supervisor would say stuff like "You're not doing anything wrong with this process but can you try doing X, Y, and Z as well?" and that would be all I got, I would try to do what they wanted and genuinely did not realize they weren't seeing improvement. They admitted in conversations that they should have done a better job training me originally on things, that they should have been clearer, that they'd given me independence to develop my own workflows on things when they probably should have insisted on doing things a certain way, etc. but everything written down is very black-and-white "employee faces significant challenges in [topics] despite coaching.")

Supervisor was very clear that a negative performance review is not discipline and does not need to be reported, but I have seen job postings from some agencies that say they may request to review performance records. How likely is it that this unsatisfactory review will prevent me from getting another job with the state? I'm still young and early in my career but I come from a family of civil servants and am very proud to be continuing that tradition.