It is early days,
I think show from the beginning you are assertive, that you are not aggressive in any way, but no push over, that you stand your ground. When they are being passive aggressive, treat it as aggressive, and push back a little so your boundaries stand. If it is a comment made, address the bit that niggles you, no matter how gently they have couched it, do the same.

Passive Agessive is the worst personality trait in business. The person who exhibits that trait is the weak link. When two people on the same team have it? It drags everyone down. They will sabotage...most of the time consciously aware that their action/inaction is a form of punishment to everyone else.

Don't feed their passive aggressive tendencies. When you see the signs? Redirect their energy. If there are two people doing it...you will have to redirect AND separate them to different tasks.

My boss is passive-aggressive. Idk any others at my work like that though. If she wants someone to not work at the store anymore, she'll schedule them for 1 work day at 3 hrs in the whole week. Someone just quit because she did that. I've only seen 2 people go. They kept calling off though. One kept stating that he hated it there. The one that hated it there, his boyfriend quit first. Only because he wouldn't shave or shower. The other one kept calling off, she was super slow, she got complaints a lot, and wouldn't smile at all. So, I can see why she did it that way. Firing them would make them eligible for unemployment.

Have you considered workplace violence?

Damn, sounds familiar, as a prior ‘immediate supervisor’ was passive aggressive. Not that long ago, there was a lot more specific and nuanced advice online than I can give from memory or experience... I wasn’t the only target, it appeared to shift between ‘we subordinates.’ With that, we agreed to organize, and “document (document, document)” the punishing behaviour we noticed or endured.

The perpetrator was a total kissass to higher authority, so they’d be puzzled as to ‘why we were having so much trouble.’ It’s damn tuff with the P/A being ‘your boss.’ I reached a ‘do as you're told’ attitude, documented well -- where I could flip through a few pages - then read their original instructions back! You get to know what’s basically a setup … so after any fresh criticism, I’d allow them to watch me take ‘additional notes’.. It never totally stopped or cured them ..but usually got them off my back, if on to coworkers…

Eventually, the P/A creep was ‘found out’ and reassigned, but after a tremendous loss of good people ~

I've sometimes wondered about using the oblivious approach, where you just steamroll them and crush their passivity without appearing to notice what you've done.

Be the opposite. Absolutely direct and upfront.

As a teacher at an independent school we deal with this a great deal. This is how many of our parents are. And since they are the customers, there is a power asymmetry. When dealing with such a parent we try to get out in front of the situation by staying in constant email contact. Always making our position absolutely clear.

Ignore them and do your job.