AITA for ghosting my annoying friend?

Hey everyone...

So here's the low-down. basically i moved from my small hometown to the big city 3 years ago with my partner, and a couple close friends around the same time. slowly but surely several more friends of friends have moved up and one of them i became friends with about a year ago. we would catch up to talk shit like once a week or every couple weeks, but were never close enough o talk about emotional or super personal things. we went to a couple music festivals together in groups as well, with my partner and other friends. This person is not someone i have a lot in common with and they had a very different background to me, they come from wealth, private school education, stable home and are 2 years younger than me which in your mid 20s does make a difference imo.

Ever since hanging out with them i noticed one of my friends distancing himself and when complained about this new friend he revealed that this was why. he can't stand this person and i was starting to feel the same way after their behaviour toward me and my partner at a music festival was obscenely rude and downright bizarre. (eg. like they were using me to make connections with my new friends since i'd been in the city longer, a lot of inappropriate touching of my partner that made us both really uncomfortable (laying on them, long cuddles from behind), we cooked dinner for them and they refused it because they had eaten beforehand even though they knew we were cooking for them (???), rude jokes at my expense in front of our friends, downright mocking me, using my stuff/eating my food/drinking my drinks without asking, and general insensitivity and privilege)

Since then (about 4 months ago) i have pretty much ghosted them, when i probably used to initiate contact 70% of the time. I don't message them, they don't message me, (probably because i ignored their last two messages) we don't hang out, we see each other at events when they come to events that I host, i say Hi, that's it. I can tell by their face that they are begging for my approval and that makes me feel bad, but i guess i have the ick.

Other than that i totally avoid them and avoid conversing with them because i don't want to be their good friend and need space, but i also don't want to confront them, so i've just disappeared. But now im hearing down the grapevine that they're really upset i didn't invite them to my recent themed birthday party. the theme was a show that they have never seen, i invited TEN PEOPLE and cooked for them all. i don't see how i owed them an invitation, but some friends think Im being cruel even though they also don't like this person, they still feel they just have to put up with them.

from my perspective, this person has treated me really poorly, and if they're upset that im not giving my energy to them anymore, they can feel free to ask me why, and im willing to politely explain why and that i don't feel we have a strong enough connection or enough in common to maintain a close friendship, but they never have reached out so... am i the asshole?

TLDR: cut off my privileged friend after they've been extremely shitty to me but never gave them any explanation and now they're being even more annoying by sulking behind my back and not confronting me.