Arent they all part of a commonwealth already?
Yes, but until the late 1940s, these nations had defacto shared citizenship and could move freely, then citizenship laws began to be introduced that created seperate citizenships instead of shared ‘British Subject’ status. CANZUK would make freedom of movement within the Dominion States (those which share the Crown) a thing again.
the commonwealth is a talking heads shop. No real trade zone
The commonwealth really doesn’t mean anything anymore these days. The nations in question do have a Commonwealth Games every so often. But that is about it. We share much culturally and politically of course, but there is not formalized commonwealth anymore.