There are commercial plastic polishing compounds. They come in various grades. I used them when I worked to refurbish electronic communications equipment for the disabled. Don't expect perfect results and work slowly and gently for best results.
Here is one example, which is NOT an endorsement just to give you an idea of what is out there.:
https://www.novuspolish.com/
Remember it is best if you contact the manufacturer yourself. Tell them what you are trying to polish and they should recommend their best product for that plastic. Use your own judgement. If they are too positive be wary.