When did Bishop Williamson approve this? Bishop Williamson refused to start any new organisation after 2012, so I would doubt such an approval, if any, would be given. Certainly I'm open to be proven wrong.
He most certainly did so.
The Canons visited him at Broadstairs and spent some time with him on at least a couple of occasions a few years ago, during the COVID era, when he sorted out their ordinations and approved their rule.
What Bishop Williamson refused to do was to be the leader of any group or organisation or to gather together the Resistance under one head.