Billing Question/VA community Care

I have coverage both through the Veterans Administration and Blue Cross Blue Shield of Kansas. In December of ’21 I had surgery it was not covered by BCBS. It was 100% covered by my VA coverage. As a follow up I had some blood work scheduled at certain intervals afterward. It was still covered by my VA coverage because it was ordered by surgeon. However my primary care doctors office even though I specified before my appointment still attempted to bill BCBS. Now after 7 plus months of telling them they billed the wrong insurance and giving them addresses and phone numbers to which they needed to address billing. I finally did it all myself. I contacted the VA. I then 3-way called with that rep and ensured they were in contact with the doctors office billing department. However, the VA says they will not cover it now because it is beyond their 180 day window to pay out claims. My question is this, who will eventually cover the billing. I provided insurance information (but they continued to bill the wrong insurance even after me telling them multiple times to remove the BCBS from my records they still tried to bill them), it was absolutely covered 100% which I have confirmed, it is not my fault their billing dept. could not figure out how to bill VA community care. Will they eat this cost or try to bill me? I assume they will try to bill me, but I do not believe I am responsible at this time.