Wireless Android Auto or Carplay generally use BT to setup but WiFi to send the bulk of the graphical data over.
That said, there are adapters to make an existing Android Auto Wireless if you want it. I think some are sold on Amazon too so you could probably try and maybe return. I don't have any experience with them since I'm very happy with my car's built in wired Android Auto and the reliability of cabling but it is something you can try.
I have one for my wife's car that has wired-only CarPlay. The dongle can do Android Auto as well. It has a bit of lag compared to wired or built-in wireless CarPlay (have used that in rentals) but it's not really an issue for usability. It was maybe $30.
Looking at image search for "2020 impreza dash" there's a screen above climate controls in all images. I was asking if there was an option to have no sceen.
I do wish it supported a later version of Android Auto so that I could run that via Bluetooth. (It does have regular Bluetooth but that's just audio.)