I can now report on my own personal experience with Google's handling of this issue as well.
After they took weeks to even just set up a website to allow customers to check whether their particular device is part of the "subset" of Pixel 6a devices affected by these battery issues, I wanted to check whether my own device was on that list.
First of all, you have to log in using your Google account just to use the service - not a good start.
Then, it asks you to enter your device's IMEI number in order to assess whether your device is affected.
When I did so however, it would consistently throw an error, telling me that there is some kind of undefined issue, which may or may not be temporary.
I then contacted Google's support, who said they had to forward the issue to some other team, and I would receive an email to that effect.
The email I actually received was a generic template telling me how to use the site (thanks captain obvious).
Once I again explained the error I got, I received an email demanding that I verify my age.
Keep in mind that all I wanted to do was find out whether or not my device is affected, nothing else, but it seems like they won't let me do that unless I send them government ID or something.
Naturally, I cannot do that, since the Google I account I have is a burner account with a fake name, to protect my privacy.
Though even if it wasn't, I still wouldn't want to send such sensitive personal data to Google just for them to answer a simple "yes or no" question.
Is there any way to tell whether a device is affected without Google, such as specific serial numbers?
As it stands, I would probably need to go down a different route making use of statutory rights in order to get compensation if my device is affected, though I have no idea where to even begin here.
In any case however, this will most likely be the last Pixel phone I have ever purchased, since I wasn't particularly satisfied with it before, but this really is the straw that broke the camel's back, as I don't think the added security of GrapheneOS is able to offset all the issues with the device it runs on, and the company's response, or lack thereof, to the issues it creates.