Yesterday, I logged in to the Virginia Department of Health site (https://vase.vdh.virginia.gov/recordrequest.html) and scanned my QR code as displayed on the site. No luck. I also tried downloading the PDF Record version and scanning that QR onscreen. In both cases, I was getting the same "Unable to add data" error you did.
I then updated my phone to 15.1, and reattempted scanning the QR onscreen on both the VDH site and the PDF Record. Still got the same "unable to add data" error in Health app. Was using a Dell monitor, btw.
Today, I tried scanning the onscreen QR again--using a different monitor; iMac--and it worked. Vax record was successfully added to Health app on the very first attempt.
So if it's not working for you in a prior iOS version, I recommend upgrading to 15.1, and also try some alternate methods of scanning the QR code (maybe even print it out and scan?) Good luck and hope it helps.