iPhone 12 Pro Max, or iPhone 11 Pro? My (alleged) iPhone 12 has identity crisis.

I have had nothing but issues with my iPhone 12 Pro Max since I bought it last December. From the camera app randomly freezing, to random black screen on Carplay, to never progressing "preparing video" messages when sending video, to the camera roll always displaying "syncing" and the corresponding battery drain, to the iPhone telling me it won't activate "unlock with apple watch" because it says it isn't on my wrist or my iPhone unlocked (they are, and both the watch and fitness apps see the watch just fine), to not being able to update OTA, because it thinks it is up to date....

And now yesterday, during my latest restoring attempt, I noticed that iTunes thought it was an iPhone 11. Then I remembered that when plugged into iTunes, the icon doesn't look like the icons from other devices, in colour and with app icons, it is just a white and grey rectangle.

That isn't right, is it?

Btw, I have tried every single method of restoring, dfu, recovery, iCloud...

When restoring my iPhone 12...