If you are able to run other OS based diagnostics, then your network is at least configured correctly.
How are you connecting this Mac you are testing to the network when running the diagnostics? You should be using the Apple USB-C to Thunderbolt 2 Adapter combined with the Apple Thunderbolt 2 to Gigabit Ethernet Adapter. Using any third party adapters may lead to failure. Reseat the cables & adapters and try using another Ethernet port on your router. Confirm other OS based diagnostics still work. Also try connecting the cables to another USB-C or Thunderbolt port. You can also try running the diagnostics on the Mac being tested over WiFi as long as the WiFi is on the same subnet as the AST2 server. If you have been using WiFi, then try using a wired connected as mentioned earlier.
Power cycle your routers since any network issue can result in a problem.
Check the GSX article for "known AST2 issues". Either search GSX or look at the setup guide for AST2 which should include a link to an article which contains the "known issues".
Make sure your AST2 server has the correct version of macOS and that it has all OS update patches installed. Make sure you are using the latest version of the AST2 software. I think the actual diagnostics are now all downloaded from Apple servers and not the local AST2 server ... not sure which model Macs this started with though. Check the last AST2 bundle to see which models it supported to know whether the diagnostics are being pulled from the local AST2 server or Apple's own servers. For some reason I think the 113 error may be related to software issues on the AST2 server, but I'm not certain...it is a shame Apple relies on mysterious error codes and cryptic error messages and providing no details or explanations for any of them. AFAIK, macOS Catalina is still supported, but older versions of macOS may no longer be supported for the AST2 server. Make sure the AST2 server is running at least macOS 10.15 Catalina and all OS patches have been installed.
You may also have a problem with the computer being tested.
If none of this helps, then contact GSX support or contact the AST2 diagnostic team for assistance. They usually won't be of much help, but you never know as maybe it is a known issue which has not yet been noted in the "known issues" article.
FYI, Being able to run EFI based AST2 diagnostics does not really mean a whole lot because it the OS based diagnostics which are more difficult to access & run due to much stricter network requirements. Make sure to try each of the other OS based tests to confirm others are working which at least means your network is basically fine although it does not rule out intermittent issues. If it is only the Full System diagnostic, then most likely that diagnostic is the one with a problem and most likely only Apple can help you as Apple may need to fix it.
