Supervisor wants me to add my name on someone else's paper to be published
Publish it. As you mentioned that your supervisor obtained permission from the original author and you will be working/editing it, then I assume its 100% ethical to put your name as coauthor and will be no negative sequences. Indeed, this kind of preparation that your supervisor follows is beneficial for you. At the level of PhD, I got the same task. I converted 3 years old master thesis to conference work and I put my name at second coauthor and the original author was mentioned before the name of the professor in the affiliation! since your supervisor is involved in this task, I assume that he knows what he is doing.