A PFA or a Protection from Abuse order is a Civil matter and not considered a criminal matter so yes the PFA will show up on a background check but not on a criminal background check.
So if you have a PFA against you then it will show up on your civil background check but not on a criminal background check.
So the PFA should not affect your ability to be able to get a job when the job runs your background or if a landlord runs your background to check to see if you're a good fit for the job or apartment.
PFA orders do appear on the civil docket as a finding of abuse, which the world can see, because the civil docket indeed public record but it's not a criminal record.