A past employer forged my signature on a paper contract to pressure me to do something that wasn’t in my original employment contract.

wow what a scumbag

if this contract service would also somehow stand up in court if I had to take legal action.

usually you have a digital trail / registration that can prove, no matter if the company is "approved" or not by any authority. You only need to prove the existence of the signature in a certain moment, like an unmutable blockchain.