Error 0x8000000000003 cannot load efi driver's test support .efi on Late 2012 iMac

Unfortunately this is a known issue which has been around since about 2016 when Apple updated the system firmware to provide access to Internet Recovery Mode which also added the online Apple Diagnostics as well. The issue is a compatibility issue with the system firmware and the bootloader files on the Apple remote server. There is nothing you can do to resolve this issue except possibly installing macOS 10.15 Catalina which will also update the system firmware. Otherwise you won't be able to access the online Apple Diagnostics and most likely you will be unable to even boot from the older Apple Diagnostics even on USB. You can try creating and using a bootable Apple diagnostic USB stick, but the same compatibility issue may still exist. These diagnostic image files at one time were (and perhaps still may be) available to download directly from Apple. I was able to use the bootable USB diagnostic on one Mac, but not another Mac which was unable to access the online diagnostic.

Here is an Apple article with instructions for creating a bootable macOS USB installer:

Create a bootable installer for macOS - Apple Support

If you used those instructions to create the bootable macOS 10.15 USB installer, then please state how far you get in booting the installer when you encounter the error. Also, try using another USB stick, especially a different brand since the quality of many USB sticks is quite poor and Apple can be very picky about the drives used for booting.