Provider claiming no coverage, but had coverage, trying to make me pay without sending a claim

I had to have emergency surgery in the spring (March). I had to retroactively get COBRA in order to cover this emergency and not go bankrupt with medical bills. The policy was active from Feb until the end of March—which includes my DOS for surgery.

I sorted out all the insurance info mainly after the fact, as I was literally in the hospital attempting to get coverage and trying to not panic. The dust settles. Finally get bills updated/claims filed. I think everyone has submitted, but surprise, I get a bill last week. It is from a provider in the hospital who has outsourced billing to a corporate sort of catch all type place who seems hellbent on not actually helping.

I explain to them via chat I had coverage. Give them the info. They state they are submitting a claim. I check my account today, it states that the claim was denied because patient cannot be identified as insured. Obviously I am not presently insured with the COBRA policy, but definitely had coverage during the period that covers the DOS, and numerous other claims are paid all related to this same visit.

What do I do? I should technically owe zero since my deductible and out of pocket were met, and had no co-insurance due, but they are telling me I owe them because I was uninsured. I cannot get them to comprehend I had coverage which termed out.

Help.