This works. In my case (or in 2026) the names of the docker bridge start with br- so the entry in /etc/NetworkManager/NetworkManager.conf becomes
[keyfile]
unmanaged-devices=interface-name:br-*
Ofcourse you have to make sure that any bridge you make yourself does not start with br-. In most tutorials for for instance QEMU/KVM it is suggested to call this br0