Let’s talk about this public place stuff exactly what does your restraining say? Does it say he must stay stay at least a certain # of yards away from you?
I would clarify with legal aid, an attorney on exactly what that means. A public area is a shopping mall, an amazement park a school sporting event, a park, etc. etc.. Which then means he can be there but it still doesn’t mean he can be near you or converse with you.
This is not a free pass for him to harass you further. I’d seek legal advice and gain clarity on EXACTLY what it means and what your rights are.
The narcissist that he is could make him believe he has the upper hand when in fact he could actually violate the restraining order and you could have him put in jail.