Base is a different process then regular ERC-20. While the no fees was tempting, it wasn't sent on the same protocol therefore never recognized. Unfortunately you're funds are likely unrecoverable, there's not anything you can do about it besides contact coin payments and MAYBE work it out with them but then again it would take manual work from them to go extract it from their ETH wallet. Sorry to hear about you're story, make sure to use the correct network next time...
Just a chill guy helping out, please leave me a like or add me rep.