I had a conversation with management and they told me I don't open up, which is fair and true and told me to be more empathetic with my coworkers.
Except that I can't and I don't care about most of them. As said, I just want to work and go home. I consider most of them childish, gossipy and immature. Of course I didn't tell management this.
It seems possible to me you've missed the message delivered by your supervisor. You plainly state here that you despise your coworkers and your supervisor is saying you need to approach your coworkers with more empathy. To me, that sounds not like you're just trying to keep to yourself, but that you're probably acting like an asshole somehow in giving the cold shoulder to everyone.
I think you're really struggling with "black and white" thinking here, to think that you would have to debase yourself and pretend to have a bright and bubbly disposition in order to be pleasant and respectful toward your coworkers. You don't have to be mean and disdainful in order to maintain your personal boundaries at work. Your supervisor might have been on to something, because developing empathy with your coworkers can help you let go of your disdain for them and will probably help you function more effectively in your role.
I worked in healthcare a long time, and the field is certainly dominated by extroverts, but I've known plenty introverts in all hospital roles who got along just fine. Healthcare is not a job you can do by yourself. You are always going to have to function as part of a team. If you hate other people so much that you're just going to move from job to job hating everyone you work with, and you feel like you have no other option than to do this, maybe consider speaking with a therapist to try to develop new ways of relating to the world instead of just being miserable.