So I found out I only had a NS entry but no A entry for my root subdomain. In order to get it work I needed to add an entry like this

However, I also want to point out that it is required to disable DNS Rebind Protection in the Router and iCloud Private Relay on your devices in order to work. I will try if I get this work with my webserver as DNS for those cases but so far I wasn't too successful.

The reason why it was working for www.local.mydomain.com was because I already had an entry like this before which I removed but I suppose was still cached on my device:

So my device tried both with and without the www and with the www it had a success so it appended it.

So I found out I only had a NS entry but no A entry for my root subdomain. In order to get it work I needed to add an entry like this

However, I also want to point out that it is required to disable DNS Rebind Protection in the Router and iCloud Private Relay on your devices in order to work.

The reason why it was working for www.local.mydomain.com was because I already had an entry like this before which I removed but I suppose was still cached on my device:

So my device tried both with and without the www and with the www it had a success so it appended it.

Setup on Webserver

So I also finally managed to move my DNS setup to my webserver. This way I do not need to disable iCloud Private Relay. My setup looks like this. (I needed to wait for a while before it was synced to my DNS and worked)

I might possibly manage to replace anothersub.local.mydomain.com with *.local.mydomain.com for wildcard subdomains but it is not really required for my use case.