Background check says I have a bankruptcy I never filed and it’s nuking my job search, what do I do now?

I’m 30F and I’ve been job hunting for about two months after a layoff. I finally got to the finish line with a company I actually liked, did 3 rounds, references, the whole thing. HR calls me sounding weirdly formal and says my offer is “on hold” because their background check vendor flagged a bankruptcy on my record. I literally laughed at first, because I have never even been to court for anything, I’ve never filed bankruptcy, nothing. I asked for the report and they sent a PDF that has my name, a previous address from like 6 years ago, and then a bankruptcy case number in a state I have never lived in. The date is from 2021, which is also the year I was working full time and paying my student loan like normal. I pulled my credit reports that night and one of them has a public record note that looks like it belongs to this case, the other two don’t. I called the background check company and they basically read me a script and said I have to “dispute in writing” and it can take up to 30 days. Meanwhile the employer told me they can’t move forward until it’s resolved, and I’m panicking because this is now the second time something similar happened, a recruiter last month vaguely said my report came back “concerning” and then ghosted me. I feel stupid for not checking sooner, but I didnt even know a random bankruptcy could attach itself to me like that. I’m not trying to sue anyone, I just need to fix it fast and stop losing offers. What’s the smartest order of operations here, do I dispute with the background check vendor first, or the credit bureaus first, or the court first? Is there some way to prove I’m not that person beyond sending my ID and praying, like do I need to freeze credit or file something official for identity theft even if my accounts look fine right now? I’m spiraling a bit because every day matters and I can’t afford to keep restarting interviews over a mistake that isn’t even mine.