It’s a really tough question, yes children benefit from socialising with their peers, but only if they’re comfortable with the setting. You sound like a really attentive parent, and are clearly doing your best to give your child a safe opportunity to mix with others, but to me it sounds like your child is a little overwhelmed by the current setting. Not every child is super social, my eldest doesn’t get aggressive when overwhelmed, but he is uncomfortable with groups of his peers, so soft play at busy times is out of the question.
There is a lot of pressure on families nowadays to opt for more formal social interactions, partly due to families being isolated from ‘their village’, and a bit of wanting to do what everyone else does. My eldest (almost 4) has always been a bit anti-social, he gets it from me, and while he doesn’t lash out, he makes it clear that he’s not happy in large groups of his peers. He is happy with older girls, or one on one with a familiar child, so we do what we can to minimise stressors and make it as enjoyable as possible.
When your watching your child, before things escalate, look for the warning signs, and what leads up to the behaviour, and then try and change the behaviour before it happens. Some of the rowdier behaviour could be an outlet for excess energy, I would take the pressure off playing with the children, and focus more on building his confidence to play in the same space as them. If you’re out, keep his attention on you, and try and tire him out, games like running, jumping or spinning will help give sensory feedback, and keep his attention from the others.
It’s tough, but some children just need a bit more guidance when it comes to socialising.