How can I store files in the mounted shared folder?

I could reproduce the problem on my system.
Your main problem are the ACL restrictions of your host.
For this reason change the ACL attributes of the libvirt-qemu user :

sudo setfacl -R -m u:libvirt-qemu:rwx /media/cl

Change the Mode settings for Filesystem /host from Passthrough to Mapped.

---

Why? That's the reason why:

Your guest system runs as libvirt-qemu user and your ACL settings restrict the permissions of this user.

user:libvirt-qemu:--x

The correct output of getfacl should be :

user:libvirt-qemu:rwx

If your primary goal is just to share files back and forth, and you're open to using TCP, you could just share files over ssh or similar.

For instance, if you re-direct a local port to a sensible port on the guest, you should be able to use that port for access. I use SSH/SCP.

When launching my VM:

qemu-kvm [all your usual qemu options] -net nic -net user -redir tcp:22122::22

And then to access the VM, I use SSH; I open a terminal on my host machine:

scp -P22122 myfile.txt klaatu@localhost:~/ssh-share-dir

fish or sshfs in whatever GUI file manager you use works just as well, as long as you set the port.