Hmm it does exist for me, actually. (On CoreOs though, not Silverblue!)
Edit: Ah no it’s /usr/share/containers/containers.conf that exists! That is the base for it, however.
Only with that set, which should be equal to not having that file existing (i.e. podman should use the default value):
#network_backend = “”
However, the podman doc you linked says:
The default value is empty which means that it will automatically choose CNI or netavark. If there are already containers/images or CNI networks preset it will choose CNI.
Ahhh… so maybe because I have old containers with CNI there, the upgrade could not upgrade these to the new netavark? Crazy… Though at which time is that evaluated?
The containers start at boot,/were created at boot so a reboot should make it choose netavark, should not it?
Edit: It also says images in the description! So basically only a fresh installation/podman reset chooses it, so if you have ever done anything with podman, it will continue to use CNI. After all that was kinda stated in their release post, but anyway… 
This is BTW confirmed by the suggestion here to look for what container packages are installed. And a fresh installation of Fedora 36 Workstation seems to work.
About CoreOS again: The link above clearly shows that the file comes with the containers-common package, at least it should:
$ rpm -qf /usr/share/containers/containers.conf
containers-common-1-56.fc36.noarch
So maybe it is better to override it at user level?
Or, as the file states in the first lines in comments, in /etc/containers/containers.conf actually. That sounds good if you want it to apply for all users on your system I guess.