1. It is your manager’s job to keep everyone productive. It’s not your job to solve, and it may or may not be useful to bring the issue to your manager; I would go with your gut on it.
2. If it were me, I would push back firmly if accused directly of not being a team player. It’s a little hard to say how to navigate it or even whether to try, from afar, but that’s my first reaction.
3. Sounds like maybe time for a new job

Your manager sucks. You’re right it’s not your job to be manager. Unless someone is being harmed or they’re doing something seriously wrong just “stay in your lane”. By that I mean do your job not theirs. If you work for a big company they may have an HR person to take issues to. Obviously if someone is being harmed or it’s a safety issue it’s your duty to speak up. Word to the wise: put everything in writing. Emailing is perfect. Got pictures? Even better. Your butt will be covered and it’s somewhat intimidating because the recipient knows its only a couple extra clicks to send it to their manager.

Make sure your work is well-documented in any way you legally can, that way it won’t just be your words against his.

You don’t say explicitly what the coworker said to you regarding you being lazy, but that is specifically what you need to address. I would go to your manager to make her aware of the situation, “xx told me he thinks I’m lazy, but I put in more hours and do more work than he does. I’m going to address this with him directly, but wanted to put it on your radar first.”

When you go talk to him, be super calm the entire time. Literally no anger, no irritated inflection. Recognize you’re likely dealing with an adult child. Your job here is going to be to make him so uncomfortable he never bothers you again through relentless questioning. “The other day, when you said you thought I was lazy, I realized I got to work well before you did that morning, and it seems like I had gotten more work done than you too. What were you basing that observation on?” Whatever his reply is, turn around and ask a clarifying question about it. “I’m just trying to understand where you’re coming from. When you sit and chat with a coworker for an hour without doing any work, I don’t bother you about it, so I’m really wondering why you’re bothering me and what that’s about.” “If we’re here to hold each other accountable to do work, I can certainly do that for you too. Do you want to start right away?”

Be super genuine and well-meaning here. He will be utterly confused and will likely realize he’s better off never saying anything like that again. You could even report back to your supervisor that you spoke with him and offered a deal to hold each other accountable to productivity standards, but he declined.

is he your superior? that is the only thing that would require you to talk to your manager. depending on the firm culture and your ego i’d consider this: you are the new one. there are minds to make up abput you. if you go and tell them about the situation, your are the one ratting others out and playing right into his hands (by ratting him out you show yourself not being a team player and - depending on management views - maybe even high maintenance). if he talks about you, he is probably already known to make quick assumptions and not shut up about those. by not telling on him, on the other hand, you show that you provide value independent of others and are not easily influenced.

try to talk to the others (carefully) why he acts that way and how they deal with it. it is normal to ask questions. you are the new joiner and just want to get to know the firm culture.

sorry for typos (typed on phone)