AMD graphics card for Mac Pro with startup screen

I have a mid-2012 Mac Pro that I want to get back up and running. I have a “patched” version of Catalina 10.15.7 installed. Right now it has an nVidia GTX680 graphics card, which means I get no acceleration. I also dual boot this machine with Linux Mint 22 via reFind. I'm having problems with the nVidia driver on Linux. This machine is connected to a 4K display via HDMI.

I want to replace the nVidia GTX680 with an AMD card so that I can avoid using the standard framebuffer on Mac OS and get around the nVidia driver problem on Linux.

Which card would be best in this case, considering…
– I need to see the start screen when I turn on the Mac
– It must be compatible with Catalina (and optionally Majove)
– I need to use the HDMI connection
– I want to use the display in 4K

I don't mind flashing the graphics card BIOS as long as I have decent instructions.