Docker in Toolbox container: File/dir permission issues

I installed moby-engine (docker) on Fedora 31 and added the docker group to my user.
I’m now able to run docker on my host.
Next, I want to run docker inside my toolboxes.
So I call flatpak-spawn --host docker run -v $(pwd):$(pwd):Z XXX.
However, all files/dirs that are created by my docker container and stored inside my podman’s volume have this user/group:

drwxr-xr-x. 5 nobody nobody 4096 Jan  6 14:46 vendor

Due to this permission, I’m not able to edit/delete these files.
If I execute the very same command with podman inside the podman container flatpak-spawn --host docker run -v $(pwd):$(pwd):Z XXX, the files/dirs have the right user/group:

drwxr-xr-x. 5 myuser myuser 4096 Jan  6 14:45 vendor

Does anyone knows, how to fix this issue?

I think it might be because F31 uses cgroups V2 in the kernel which is not compatible with docker runtime yet.

OK, I see.
Might there be any workaround to have my containers user/group when creating files/dirs by the docker container?
Normally I would simply map my host systems docker.sock to the podman toolbox container. However, the Toolbox cli tool does not provide this functionality.