I have tried .1 and .2 of .20 and will not launch. I have attempted to reboot the PC but with no effect other than the same issue will persist. All steps have been followed for AXIOM as I have requested support for them too, but with the API executable not working, I cannot go any further.

Fabric API jar file is not meant to be executed on its own. Instead the file must be placed within the mods directory of your Minecraft installation. See https://fabricmc.net/wiki/player:tutorials:install_mcl:windows