I can't see how a styrup will help because the joint between the styrup and the post will not be any better than your rotting post for rigidity. There was an Australian company that made a steel post repair which fitted around the post, was driven into the ground and then coach bolts used to attach the post. I used them to successfully repair a fence like yours some decades ago. I'll try to remember the manufacturer's name.
Edit: not the ones I used, but Google Strongtie E-Z Mender fence post repair.