Since we're only being told one side of the story, and issues of bullying are often subjective (it is equally possible that someone could be actually bullying as it is that the other person has a thin skin and needs to learn to take criticism), it's difficult to give an impartial answer to this question. So I'm going to give 2 answers and you can choose whichever one you like:
One possibility is that this is actually bullying. This is not OK. However, as a developer yourself, "team morale" is not really your responsibility, and everyone knows that. If you go to the other team, or their boss, or whoever, and say "my team doesn't like this", then you won't be taken seriously. You need to go up your own chain of command to people in your chain who are responsible for that sort of thing. This will likely be your direct manager, or perhaps their direct manager; you don't have to go too far. If they are not present in the meetings where these issues occur, let them know there are concerns (and what those concerns are, you can repeat what you wrote here), and ask them to be present in the meeting to observe next time. If they are already in the meeting and they know about the issues, raise that these are issues you want handled; it could be that your manager doesn't know these comments are problematic and thinks everything is fine, so make it known that this isn't fine and something needs to get done. At that point, if your manager refuses to do something about it, it might be time to find a new manager. Surely, if the entire development team quits over their treatment by project management, then PM will quickly find themselves in some hot water, as they don't have people to do the tasks; at least now they can say the tasks are being done but not up to specifications, but if everyone just up and quits, they won't even have that. So it's in everyone's best interest to get this problem resolved without losing the whole development team.
Now, it's also possible that the premise of the question is exaggerated. You didn't provide any direct examples of things that were said, but only said that some comments were "passive-aggressive". You also said that some of the comments made do have merit, that mistakes are getting made. Now, since above I defended your position against the PM team, I'm now going to defend the PM team against your accusations, just to be fair. If your work is not up to expectations, you need to work on that. I'm assuming this is not the first meeting the PM team has made complaints; if they have to constantly come to you and constantly complain about the same thing over and over and it never gets fixed, well that builds frustration. It's no excuse to intentionally bully someone, but sometimes things just get said that maybe shouldn't get said or shouldn't get said in the way they are. It's also possible that things get considered "passive-aggressive" when they actually aren't, for example if a bug is pointed out as high-priority, and then it doesn't get fixed, and then it cascades into another bug, then the PM team might say "well, we marked this as high priority for a reason"; to some people that might be "passive-aggressive", to others, not. However, it is a true statement: If you fixed the first bug as high priority, then the cascading bug wouldn't have occurred, and PM team did tell you it was high priority and you dropped the ball, so they kind of have a right to be upset. In this case, you have to rebuild trust between your team and the PM team; PM thinks you're incompetent, and they're more or less saying it to your face. Complaining about it to management, if you take the above advice, isn't going to solve the problem. If you take such an issue to management, they're going to say "PM team is telling you you're incompetent, and based on XYZ metrics we agree with them, so shape up or we'll fire you", and that's if you're lucky and don't just get fired on the spot.
Take a step back, and think about the situation logically: If you remove yourself from the immediate situation of being on one team and biasing your opinion towards your "in-group", do you think it's more likely that PM team is acting belligerently for no reason, or do you believe that your team is dropping the ball repeatedly and giving PM team a reason to be mad at you? Take a minute, reflect on that question, and let that guide your next steps.