Idk if this will help, but I barely managed to install my printer with the same issue, using HP Easy Start.
Actually the program didn't detect the printer, but when I install it, suddenly on my Windows' printer and scanner settings, I can see the printer driver being installed.
For me, the USB connection doesn't work, only the wireless.
I tried HP SUPD too, but for some reason it didn't work for me.
Oh yes, and print using Print System Dialogue will help if you get MS Edge spooling issue.