How to de-escalate a situation when a user balances on the edge but others who want to correct them go beyond the rules?

I believe you posted the determining factor in your question, with "Comments themselves do not seem to violate rules of the site." It is important to follow policy. If the policy is bad, it should be revised. You may be in a position to revise it, or just in a position to advocate for a revision. If you feel strongly about it, you should do that.

In short though, you appear to not like your site's own policy... You believe someone is not behaving appropriately, yet the policy says he or she is. If you are not in a position to revise the policy, you have to let that go. In a professional environment, you don't get to arbitrarily make rules for one user that are not announced for all. And that is effectively what you appear to be wanting to do.

Regarding the others... You also stated the decisive factor in your question. You clearly believe some of these do violate policy. I assume your policy proscribes action to be taken when a policy is violated... So what do you do? You take the proscribed action. Hopefully, this just means telling the person "Personal attacks and name calling are not allowed. Please keep it on topic."

This is going to be hard if you know and appreciate the typical input of the users you are policing. But you need to remember that you are in fact policing the site. Your job, at least in this regard, is to apply the policy fairly and equally regardless of your personal relation to the members there.

All of this said, you can do the above in a nice way. When you tell someone not to name-call, the person might respond, "But he started it with (whatever)". You can use that as an opportunity to explain that while the other person's opinion was stated bluntly or harshly, it wasn't a personal attack. And the policy of the site draws a line at personal attacks. That's why your comment was removed, but the other person's is still there, etc.

Good luck.

I've been the user leaving comments before. There are a couple of things worth bearing in mind.

First off, the user commenting in all likelihood doesn't realize that their comments are coming across as curt. This often happens when there is a large amount of these low-quality posts. It's not really sustainable to write a personalized comment for a hundred different answers, so one thing that users do is to create a stock comment, and post that with minimal edits on each answer. So you've got this user leaving this stock comment, that they don't realize is curt, on a bunch of different posts.

Then, you've got the user on the receiving end of the comment. They don't know that it's a stock comment, so they've just gotten a comment pointing out that their answer doesn't meet requirements, which stings in the first place, and the comment is curt, to boot.

An overworked, tired user and a frustrated new contributor. Not a good combination.

Of course, neither of these people actually have an excuse, so you do need to deal with the situation. What's the best way to approach it?

If things are ongoing, the first step you need to take is to stop the immediate situation. If it's happening in chat, or comments, and things are degrading, you need to stop the immediate situation - essentially separating the users. This could be achieved by simply deleting the comments, or locking the post, or freezing a chatroom, or trashing messages, depending on what seems like the best option at the time. Try to keep it impersonal, and consider telling them that you'll reach out to each of them personally.

Second off, reaching out to the offended new users would be a good next step. Apologize for the curtness of the previous commenter. Acknowledging that there was a misstep is always a good idea. Once that's done, you can explain to them that even if the other person was curt, being out of line in response is still not a appropriate response. If it seems like it could end productively, work with the user to help them improve their answer or whatever.

In addition, reach out to the commenter. Explain that their comments have been curt and could be improved, and that they need to improve it a bit. Thank them for the effort they've been putting in. Including praise and gratitude is a great way to get them to be more receptive to what you're saying - just telling someone off is unlikely to be received well. Make sure to balance appreciating what they're doing but informing them that they need to improve things a bit.

Of course, things will be dependent on the exact situation. In your position as an exception handler, you'll need to make a judgement call about the specific circumstances you find yourself in and what steps need to be changed.