Is this related to the authentication issue with the gpg error? Do you still have that?
If I understand you correcttly, you installed Docker on Arch Linux, then installed Docker Desktop. Docker Desktop create a virtual machine and adds a new Docker client. It can also change how the client authenticates. You can switch between Docker Desktop and the Docker daemon installed on the host by changing the context:
docker context ls
docker context use CONTEXTNAME
When you use sudo su, you have different contexts without docker desktop.