Error: 0x8000000000000003, Cannot Load 'EFI/Drivers/TestSupport.efi' encountered while trying to run diagnostics

Unless you can upgrade macOS to a newer version, then there is nothing you can do about this error when trying to run the Apple Diagnostics. A system firmware update to your Mac has rendered the system firmware and the diagnostic boot files located on the Apple server to be incompatible. Apple would need to either update the system firmware or update the diagnostic boot files on their server. This issue has existed for many years now, so I would not expect it to be fixed by Apple after all this time.

If you are having problems with your Mac, then there are other ways we can help you to diagnose the problem. You will need to provide the exact model of the Mac and version of macOS used as well as some background of the problem and the symptoms. If the Mac can boot, then running EtreCheck and posting the report here using the "Additional Text" icon will help us assess your computer. If necessary we may also be able to provide other methods of checking some of the hardware depending on the problem and the exact model of Mac. If you cannot boot normally, then try booting into Safe Mode.

Here is another Apple article for troubleshooting various startup issues (Apple assumes everything is a software issue unless all steps fail to resolve the issue or a clean install fails):

If your Mac doesn't start up all the way - Apple Support