You're the nurse who couldn't deal with extroverted coworkers and had to leave your job, right?

Respectfully, you should learn from that experience that your hardline introversion doesn't serve you well in the workplace. Any manager will be more interested in preserving team dynamics than coddling a brittle individual. I don't mean to be harsh but you need to learn a little flexibility or you're going to run into the same problems again and again. You picked a people-facing career and chances are high that most of your colleagues will be on the extroverted side.

It's fine to be introverted but you need to communicate your needs in a way that doesn't alienate or offend your colleagues. It sounds like you want them to meet you where you are, rather than compromising somewhere in the middle. It won't kill you to make a couple minutes of small talk, followed by a polite excuse as you remove yourself to be alone. You can even say something direct, like "I don't mean to be rude, but I'm not huge on chitchat, and I have some studying I need to catch up on." People prefer honesty to just being iced out.

You can't expect them to respect your feelings and preferences if you're not willing to do the same for theirs.

So right up front, you want to inform your supervisors that you won't work with two of the long-established members of your new department because they don't meet your personal interaction standards? And you think that's going to go well for you?

If someone came to me with that demand before even starting the job, I'd breathe a sigh of relief that we discovered their weirdness before it was too late, and choose another candidate for the job.

Welcome to the working world! You don't get to choose who you work with, you just have to make the best of it. If you need this job for advancement, then focus on that, and put up with whatever else goes with it, like EVERYBODY ELSE. Who told you that you could go through life without the minor inconvenience of having to deal with conflicting personalities? This is Real Life, you don't get some protective bubble from the icky, inconvenient parts.

There's no scenario where I would bring this to a manager. If you aren't capable of (politely!) setting your own boundaries with your coworkers, you're going to struggle no matter what team you land on.

I suspect, given this is a medical setting, the hiring manager has more important things to worry about than "are people talking near the new person again?"

If you came to me with that demand before hiring I would thank you for your time and wish you luck finding a position that meets your needs. I have my own shit to deal with, training new team members is already an additional load to take on, and having to manage personalities full-time is not in my bandwidth

Why don't you tell these two "experts" to shut up and leave me alone? Do you really need a boss for that?

It's the company's duty to provide you a workplace.

It's not the company's duty to provide you a workplace where all people are perfect.

So you are trying to play the entitled one here. And I am sure that is not going to be successful.

You can't run away from people like that. Get rid of those two and more just like them will take their place. Any demands like this are only gonna let your soon-to-be supervisor know that you are difficult to work with. Which it sounds like you are, with all due respect.

I get it, I'm the introvert too, but it helps to understand where they are coming from...

For them, these inane conversations are likely their pressure/stress release. Medical gigs can be pretty high pressure and everyone reacts to that differently.

I've only witnessed it from the patient side, but I get where it's coming from.

When I had my first heart attack, it was just after Thanksgiving and the cardiac ward was decorated for Thanksgiving. They had these "Guess the heart rythm" charts made out of tinsel, and I got to see them all as I walked the ward after surgery.

(Bonus, immediately after open heart surgery they make you get up and walk around multiple times a day.)

The chart right by the nurses station? I wish I had taken a photo of it... tinsel flatline ending in an angel. LOL.

Are you considerimg turning down a promotion (with more pay or progression to more pay?) because a couple of coworkers talk too much?

I would rather space out while they gossip and daydream about all the extra money I'm going to make.

I would absolutely not raise this concern with my boss. Since my job includes needing to work well with all kinds of people, raising your concern would be career limiting, for me.

If you absolutely demand change you need to have an answer to allay the manager's fears that the changes you require will be a net negative for the group; that unserious gossipy annoying group that is setting the current bar for success.

From the inane gossipper's perspective you could appear easily distracted, argumentative, and unserious. You've declared that their stress management rituals may be such a hindrance that you'd reject a promotion to avoid participating. That answer could gain you enemies even if you don't even interview if it's not kept confidential.

I hope this is received as contingency planning and not an insult. I don't think those things and I also hate work gossip, but in this scenario you're the out-group until you get in. It behooves you to become a quiet friend instead of gossip fodder. I hope you can play this field successfully and good luck!

If you aren't willing to work on your social skills, you need to stay in a position where you don't need them.