Replace your GPU if you want support past High Sierra.
It's a GPU to old to even have OpenCore GOP support, if you find an updated GOP firmware for your card you could make it work with OpenCore and up to 10.13.6 for pre-boot configuration support (boot screens/boot picker), but without driver support after 10.13.6 the card won't work with Mojave/Catalina/BigSur after the AMD drivers are loaded during the boot process, black screen.
P.S.1: Maybe with Mojave/Catalina/BigSur and OpenCore you can get the EFI drivers to work, but the display will be completely un-accelerated and it's not useful for anything besides diagnostics.
P.S.2: OpenCore can work with a Nehalem Xeon via board-id spoofing, more or less what people with MP3,1 do, but native updates won't work via VMM flag spoofing. Replace your Xeons, it's too cumbersome to work around Nehalem limitations.