Unfortunately, too little information, so I have to guess.
Actually everything should work if it worked with the old Fritzbox.
If you are on the “Current status” page, which brings you to the “Edit” page, where you can click on “Set current address”, you can see that both pages say “IPv6 prefix”. So it is normal that there is only “the first half” of the IPv6 address, namely the prefix. If you click on “Set current address” on the “Edit” page, the entire current IPv6 address is displayed there (prefix + host part), but the one from the computer from which you are calling the website, not from your server or your Fitzbox. However, only the prefix is used.
The IPv6 address is set on the “Resource Records” page. There should be an AAAA entry named “yourdomain.dynv6.net”. If you click on “Edit”, the name should be empty and the complete IPv6 address of your Fritzbox should be in Data.
Your server should have an AAAA entry called “yourserver.yourdomain.dynv6.net”. If you click on “Edit”, the name should contain “yourserver” and the data should contain the host part of your server ("::xxxx:xxxx:xxxx:xxxx").