Cannot connect to the Docker daemon
Previously flawless working docker daemon was marked as not working not only in PHPStorm IDE, but also even in Docker Desktop / Settings / Builders. After some research, thanks to StackOverflow answer it appeared, that company decided to remove automatically creating /var/run/docker.sock in MacOS specific version starting with the release 4.13 of Docker Desktop. The fix provided under the permanent solution header resolves the issue:
sudo ln -s ~/Library/Containers/com.docker.docker/Data/docker.raw.sock /var/run/docker.sock