I believe the issue is something like this: Eirikr70
Originally I received the same message. That my Pixel 6a would be ineligible. After asking why, I was told to install the stock OS in order for them to confirm that the IMEI I provided belongs to my Google account. After I did they were able to verify my device and I received the money.
I've described my experience before here https://discuss.grapheneos.org/d/27443-pixel-6a-battery-warning/14
Perhaps they want to make sure you still own the device you are requesting the compensation for. That you haven't sold or scrapped it. After all their goal is to get the defective batteries out of use.
MetropleX I'm curious. Did you choose Google credit or cash payout, or the replacement by a service center? Maybe they are less restrictive with the latter, since the service technician can verify the phone/battery. So they don't need to do it remotely.