There was no compatibility problem, Google intentionally blocked the installation to avoid reviewers testing the chip. The benchmarks worked without issues when sideloaded, but not every reviewer bothered to do that.
Sounds like a compatibility problem. I don't understand how exactly the play store works, but if your device string is unexpected (like maybe a new device? or a lineageos phone) some apps can't be installed from the play store but work fine sideloaded.
As a side note to this, Aurora store is awesome. If you sign in with your Google account, then you can install paid apps that you've purchased, but the Play store thinks are incompatible with your device. In my experience, the majority of them work perfectly fine!
I think you are as blind to Google’s intentions as much as I am, but it sure seems silly for them to intentionally block it from the Play Store when side loading it is trivial, doesn’t it?
Apparently Pixel 6a owners also had this problem, but with none of the Tensor G3 performance speculation in the article: https://www.reddit.com/r/GooglePixel/comments/wc4m3w/pixel_6...