What are some tips for handling confrontation at work for someone who’s naturally averse to confrontation?

You may want to research emotional intelligence. There's lots of methods you can try but they are not quick to explain. Some examples.

Ask to explain, clarify. Someone made a derogatory comment - call it out. E.g. What do you mean by X? Are you implying that Y?
Dont get angry. Provide clear incentive to act. Increase the cost of failure. Can be as simple as CC relevant person in the email. State clearly what are the expected outcomes. Highlight the risk. Make sure others know what's going on.
Question real reason for the criticism. Is it really something in your control? Ask what they would do in such scenario. Dig into details. Point out gaps

Above all stay calm. The more the other person gets angry and confrontational while you stay calm and professional the better you look in eyes of everyone else. It makes it obvious to others who is the big baby and who can the handle pressure.

This comment ^ is the best advice. In all conflicts, it is of the utmost importance that you stay calm.

However, keep in mind that this will often infuriate or enrage an aggressor. Often an aggressor is endeavoring to provoke you so that you lash out first. When you lash out first, you lose.

I have always had a huge difficulty controlling my emotions in these situations, and so I always tried to avoid conflict. Now, I am married, and so conflict is unavoidable. It is imperative that I control how I react and respond.

I still struggle with this. I actually wish that I had some coaching on how to manage my anger, but I have had to deliberately get better with practice, and it has been hard, and sometimes even embarrassing.

Edit: One thing that I have found that helps sometimes is explaining to an aggressor why you are feeling angry immediately as you feel yourself getting angry. If something is said that hurts or offends, say so. Say, "You said that I do X, or that I am Y -- that feels unfair, inaccurate, and maybe even as though you are intentionally trying to hurt me. I wish you would find a different way to say that."

If the conflict is with a person operating in good faith, this often leads directly to an apology. If not, then you might be dealing with someone who is in fact intentionally trying to provoke you. There is no need to disclose your feelings further to such a person, but it can still be helpful to understand the nature of the attacks from which you are defending yourself.
- I can absolutely relate to this! Thank you for your perspective!
A+ advice. I was not taught great conflict resolution skills as a kid and have some neurospiciness that makes regulation challenging at times, but my meds help and I think I’m better equipped emotionally these days than I tend to think of myself as or give myself credit for. Thank you for the advice, this is all A+ insight.

I don't think it's the best but in such cases, I personally take the minimalist approach.

Keep all communications on official channels, and only send precise and to-the-point messages with as much brevity as possible (of course, make sure that your points are clear and that you are responding to their main queries as well). Make it as if they're talking to an intelligent robot.

Nothing wrong with this. Professional and concise, like every email should be.
- This works very very well for me as well.
  
  Make sure every point you make is objectively sustainable and don’t deviate from the truth. People hate having rock-solid bullet-pointed lists describing why they’re idiots chucked at them.

De-escalate emotional tension. Don't get personal. Don't make sweeping statements or promises in the heat of the moment.

Great advice

I don't like confrontation either but it is important to set boundaries. I've done this. It's okay for someone not to like me but I will not tolerate disrespect. I had somebody at work call me stupid because I could not solve their problem right then and there. When I get very angry, I speak quietly and enunciate my words. I said to this person, "I'm going to leave now. You let me know when you're ready to work with me." To which she responded that she would call me and I retorted, "No, you will not call me. You will send me a Teams message or an email." And I walked away. Naturally I got accused of all kinds of things but I documented what happened and signed and dated it. HR found in my favor.

This hits close to home. When I was candid about the fact that it took some courage to speak up about something that needed pushing back on, I got called a “scaredy cat” 🙄
- Name calling is the language of the weak. I it does take courage and I'm glad you summoned the courage to do so.

The advice I give to all my colleagues (and family) is this: you can’t control the behaviours of others, which means situations can go to places you were not expecting. So for me rule number one is to write everything down. Dates and times and any incidents or interactions that you’ve had. All communication with the other person through official channels and if you need to speak either do it with witnesses, and I know sometimes that’s not possible, so write everything that’s said between you down. If you can do it while you’re meeting with them great, otherwise straight afterwards. Sounds like a lot of work, and it is, but depending on what happens in the future it can save you a lot of heart ache

Thank you!
it can save you a lot of heart ache

*headache

Was probably what you meant
- Actually it could be both - I have experience of both

Lacking a bit of context to understand what the problem is but perhaps look into "nonviolent communication" its a nice way to take feelings out / address them without resolving via emotional conflict

Mostly a new manager on our team causing issues (not my manager, half our team is her side of the org chart, my half of the team is a different skillset & manager.) She is not my bosses boss either. For some reason she is convinced she is both of those (boss of the whole team.) For context this is a very small team with full time focus on a special subsidiary co of one if my employer’s main clients. We are six people total, so theres no avoiding her. The rest of us do have and have always had a great dynamic and working relationship, but this woman respects nothing but the sound of her own voice, has no idea how to listen or compromise, doesn’t know wtf she’s doing, and thinks she’s going to bully everyone into doing things her way regardless.

If she has any experience in our industry, its very outdated. This does not stop her from being convinced she knows better on how this team works than all of us who’ve been on it for over a year. Lots of weird petty authoritarian control issues. Fixating on tardiness (its not a formal policy, but we work in a “younger” field and have always operated on a “as long as your deadlines are met, nobody cares if you’re running late” policy. This has become a whole crusade for her.

We have a short daily status call and try to all meet in person for it every Wednesday. She tried to insist these calls need to be in person everyday were in office (we hybrid.) Weve already pushed back on it, now she’s insisting these calls become video conferences 🙄 presumably so she can confirm we’re all at our desks on time.

Trying to make a lot of arbitrary (and sometimes counter productive) changes to processes shes not involved in, signing my half of the team up for ad hoc special projects from other teams for brownie points for herself, etc.

None of this would be so terrible if my actual boss weren’t utterly paralyzed by confrontation. He claims he’s biding his time until she really steps out of line, but I think he just has no back bone. Confronting authority figures (actual or imaginary as in this case she’s not my real boss) is stressful to me, but once I initially broach the topic, I do okay and keep it professional/constructive, so I’m trying to pick my battles because we’re all sick of being bullied by this idiot and I’m tired of waiting on my boss tk say something.
- Sounds to me like you feel stressed and perhaps angry because you'd like there to be clarity of who has authority over what/whom.
  
  As has been pointed out in a different reply, try to not think in terms of whos right and wrong but try to deescalate the emotional tension I dont know "emotional intelligence" but in "nonviolent communication" it goes along these lines:
  
  Listen. Try to understand what she wants how she is feeling. IMPORTANT: A feeling is not an accusation: Eg "hurt" implies someone hurt you. Dont feel accused in such a case, you just havn managed to find the right feeling yet. Dont tell her, her feeling is wrong, just find the right one (accusations never help)
  
  Try to find out why she is feeling this way, whats her underlying need? IMPORTANT: A need does not depend on some specific person. If she says "I need you to...", continue digging. Again, no accusations, that would cause only problems, you try to understand something here.
  
  Reflect and refine your understanding, you can make guesses if you make clear your asking to understand. Eg "it seems to me you are really enthusiastic right now. I take it, project X is very important to you and you want to make sure everyone pulls in the right direction?" Dont fake it, you really have to try and understand her, you dont have to agree.
  
  Rinse and repeat until she feels understood (usually easy to notice).
  
  Turn it around: Tell her your feelings and needs behind it. Same rules apl ply.
  
  This is an ultra condensed version, I recommend watching: https://youtu.be/l7TONauJGfc
So I already pushed back on some of her unreasonable demands already, and essentially I’m trying to ready myself for more little skirmishes even though it scares the shit out of me. My boss has assured me she has no authority over me and the org chart shows that plain as day, I’m just not used to telling someone who is technically higher ranking than me no in polite and tactful ways when appropriate. This team has been such smooth sailing (interpersonally) up until now.

Are they averse to conversation? They might not like to talk. But you might find that if you are feeling a person doesn't want to communicate, it might be because you are not communicating well either. You need to use your own skills and take initiative.

I can point you to several skills.

https://dbt.tools/interpersonal_effectiveness/dear-man.php

https://www.practicalrecovery.com/prblog/family-communication-be-pius-this-holiday-season/

Be very gentle using any interpersonal skills. Only ever speak from "I statements". If it doesn't work, it wasn't meant to work.

I am the “averse” one- meaning, I have a hard time setting firm boundaries, struggle with gathering the courage to say no, etc. The person in question I’m having to push back against is kind of passive aggressive/manipulative, but seems very confrontational.
- So why are you talking to them? Part of being a good conversationalist is knowing when to drop it.
  
  I think (I am a shit head on the internet) that this might be telling you something. To reaffirm those boundaries you already know about.
  
  Talk to them or don't, but remember what is important to you personally.
These links are excellent! Thank you!
But I’m very sociable amd not shy with conversation!