Billing statute of limitations

This isn’t a current crisis, but I’m curious, what’s the statute of limitations for doctors billing patients or is there a link to a state-by-state breakdown? For context, last year, I received a bill out of the blue for $365 for lab work I’d received while I was covered by my previous insurance company, BCBSIL (I am no longer covered by them) two and a half years ago. I had never received an EOB for the service since they didn’t have my new address, so I called BCBSIL and they struggled to give me a coherent answer as to what happened since the account was so old. The first rep I spoke with suggested that the office had double-billed me and I didn’t owe anything, which didn’t make sense to me. However, I finally spoke with a more informed rep who explained that the doctor’s office had submitted a claim back in April 2019 and had been paid at the time, but then submitted a new claim in 2020 because they had forgotten to bill for a portion of the services I received. BCBS requested the office pay them back for the initial payout, and asked for more records. By the time the whole thing was resolved, it was August 2021. I called the doctor’s office and hard-balled them, saying that, at the time, I’d never received an EOB and I wouldn’t pay until I had more information. They said their billing department would look into it, and the charge has since disappeared from my account. I’ve also kept a close eye on my credit report, and I haven’t seen any evidence of the charge. In hindsight, I received the EOB after requesting it from BCBS and I think the office did have the right to charge me, but what is the statute of limitations for patient billing in Illinois? Would this count as a failure to bill my insurance in a timely manner? Could the office theoretically try to charge me again, even though I’m now going on three years from the initial date of service?