Have you tried to install an older version of Docker Engine just to check if that works? I installed Docker Engine on Arm, but not 24.0 yet, only 23.0 and I used an Ubuntu VM, not Debian.
Searching for the error messag about iptables I found these
- docker-failed to start daemon: Error initializing network controller: error obtaining controller instance · Issue #1105 · docker/for-linux · GitHub
- Failing to start dockerd: failed to create NAT chain DOCKER
- linux - How to resolve `Failed to create NAT chain DOCKER` as Reboot not working? - Stack Overflow
Do you have any security software on Debian? Firewalld and AppArmor are mentioned on the net as well, and someone just updated the APT packages on the OS which fixed the issue. I found this in the release info of Docker 24.0.0
- Remove workarounds for obsolete versions of
apparmor_parserfrom the AppArmor profiles. moby/moby#45500
I don’t know if it is related, I really just did a quick search and shared the links.