Should I apply for a second masters degree (PSI master's program) after already having done a dual degree in physics?
I would say if you apply and are successful then it would be worth taking, I think the program in general is well-regarded but if your worried about it looking weird to have two masters degrees you could refer to one as physics and the other as theoretical physics. The program is very challenging to get into but it covers lots of material in theoretical physics, though goes through this material very fast (and the entire lecture series is online).
You will also get to know all the other participants well which will be good for networking in the future, and you will get to meet a number of well regarded researchers in theoretical physics (and because of the reputation they will probably be more likely to keep an eye on people who participate in the program).
The only thing that comes to mind is that it is possible PSI may be looking for students who don't already have a master's degree, but I have no knowledge of that and it if it is an issue, then its not an issue with respect to your ultimate goal.