I found this problem after updating a certain version of iPad OS 16 beta too. The HDR option disappears when watching YouTube via Safari, but the app version still provides HDR. I think either it’s a bug of Safari, or Google has banned browsers with Mac UA from getting HDR contents(iPad uses exactly the same UA as Mac). And the issue still exists till now.
You may change your UA to Chrome/Windows to find out if it is caused by the UA issue(iPad’s Safari can’t change UA so I can’t configure it 🙁)