Have you done a sensory profile for your son?
The thing with calming vests is they apply pressure to the shoulders and chest, and it appeals to the sense of proprioception.
If your child is not a proprioceptive sensory seeker, then they will most likely not work. Even if he is, there are different kinds of proprioceptive input.
There's the sense of weight, which is typically how calming vests work, and they're good for children that like to be held tight and squeezed, and then there's things like sensory socks which don't provide weight but they provide tension which gives more autonomy. The calming vests can feel overstimulating and they can be hard to remove on their own and that loss of sense of autonomy can also be quite upsetting, but for other children it adds a sense of security. My son loves his, but he also loves being strapped into his car seat and the straps pulled tight, and the same with his pushchair, and he will crawl under all 100kg of me just to be crushed.
You can get sensory pods, which are inflatable, and they provide the pressure, and the autonomy, but they can only be used at home. Weighted blankets also provide the weight and you can get small ones that are more portable, so they can easily be put under a buggy or in a back pack.
A childrens back pack filled with slightly weighted things can also give a similar sensation to the calming vests, so I'd try that first, because like blankets, they're easy for the child to remove on their own when they're overwhelmed.