After some evaluation and tinkering with sympa which I finally got it working. Nevertheless I decided to give mailman3 a try because sympa just felt a little unwieldy. I just want to mention the api based on web-services.
I've installed mailman3 using https://github.com/galaxyproject/ansible-mailman3. This worked more or less. There was some issue with the python/django version and the latest release of mailman3 which has been resolved with the latest release 3.3.9 of mailman3.
There is only one thing you need to do manually after applying the role ansible-mailman3 first which is to add 'allauth.account.middleware.AccountMiddleware' in the MIDDLEWARE array in /opt/mailman3/lib/python3.10/site-packages/mailman_web/settings/base.py and run the role again.
I've created an additional ansible-role to do the necessary postfix changes: https://codeberg.org/ansible-galaxy/ansible-role-postfix-mailman
Hm very strange. After I've opened "System Settings" and enabled "Hide incompatible settings" it works. But I had some problem to save "System Settings" again afterwards. I got the message: "Invalid MySQL host address: [<public ipv6>]". The latter seemed to be caused by one or more entries in "MySQL-Access-Hosts". After I've removed all public ips (v4 and v6) - which are not reachable anyway because of firewall-rules - I am able to change and save settings again.