What you report is unfortunately fairly common. I have been in similar situation, which I will detail further down.
My first advice is:
Whenever you're being stalked by an unprofessional individual you must gather evidence of the harassment. There's no excuse for not doing that in modern times. You know your abuser, so have a recorder (e.g. your smartphone) ready and turn it on as soon as contact begins. Keep records of threats, insults, abuse. Had you recorded what you just described, you'd now be in the advantageous position. If you haven't documented them yet, induce the threats to be made again so you can record them somehow.
Second advice: Usually PIs are way less "powerful" than they have their students believe. The typical professor barely knows any faces outside of his/her own department. Exaggerating a couple of cold emails exchanged with "being friends with" other more influential professors is common practice. Anyone who's truly influential needs not to make any threats. Bullies are usually just weaklings, acting. So, stop believing this person, completely.
Keep your distance from this person. You're psychologically affected, and the abuser can see it. Only come any closer if you want to gather incriminating evidence (feel free to act), otherwise just completely shun from any interaction.
This includes your professional sphere. You must move away from this person also professionally. As mentioned in advice 2, you'll be surprised to find out that nobody knows this person in so many other circles just around the corner. Attending this specific conference was a mistake on this (surely there are so many others where you'd be way more comfortable), but alas, now you're there just do your best and avoid the maggot.
Fourth and final advice:
Stay awesome! Present your work, don't give undue credit to anyone, nor keep any collaborator in the dark. Enjoy your conference, make contacts, reinforce ties, meet new peers, smile, dress well, keep your head up. You're an independent scholar, you believe you have great ideas to share, so do it with great style. Your confidence will naturally attract good colleagues and keep the fake ones and vampires away.
Some of my experience: (i) feel free to read my fairly recent question where I had to deal with toxic ex-colleagues in a large conference. Everything worked out just fine. (ii) also as a PhD student I had a bad supervisor (though probably not as bad as yours) who wanted to either sabotage and take credit over my projects. Once I was set to attend a large international conference, and I submitted a work completely of my own without adding his name. He heard about it from another professor, so I vaguely apologised having made some confusion and just pretended to correct it. I knew how the conference proceedings worked, he wouldn't be there, and saw he'd never really check (fuzzy to find, foreign language, online-only, too many pdfs, etc). I then just handed him pdf files with his name showing, for the text and poster. In reality it, it didn't. Nowadays I feel is childish and risky and I don't recommend you do exactly the same (I was outraged), but the main message is: you don't play fair on bad guys.
Have a good conference!