I suppose it is tar version dependent, but on any recent Linux version I have used, you can just tar xvf <tar_name.tar.{z,gz,xz,etc}> and it will automatically figure out if it is compressed, what tools were used to compress it, and how to decompress it.
But you are right, x and c are mutually exclusive.
Fedora is systems, right? The easiest way to gain some (temporary) space is to clean out the journal and whatever logs you don't need. It can grow quite big.
sudo journalctl --vacuum-size=100MWill shrink it to something manageable. This will buy you some time to clean up until the journal grows again.
Also, clearing the apt cache will probably help free up some root partition space
sudo apt cleanYour root partition where packages are stored and all the logs and transactional databases might be full even if your home directory has tons of free space.