Sometimes the first step of a lawsuit is discovering who you're suing. It's not unusual and there are processes for it. You could bring something like an access log to a court and receive an order for all ISPs involved to unmask the corresponding users.
Bright Data's business is legal, but they could be subpoenaed to find out which customer is making these requests, but first you would have to prove they were actually involved, because there are many residential proxy providers.