Ok I spoke with my accountant today and got clarification for my situation, I hope it helps you! If I am a sole trader, I am able to work for US clients and also contract people from the US as long as I am physically in the UK when doing all of the work. It doesn't add any complexity to my taxes, but I had already hired them on the basis of needing to do business taxes, so I'm not sure how it changes them from a regular return.
If I were to become a limited company, then I'd have to set up as an official company and pay myself via dividends or salary. This makes US taxes complicated since an LLC would be taxed as a person in the US. We didn't get too far into this option for now, but I think it involves having to incorporate in the US as well which makes taxes and legalities complicated.
My guess based off what they told me is that you'd be good to take contract work for the US company if you're a sole trader, it might just mean some extra business tax forms. But I'm not an accountant and have learned through this whole process that it is a big ol' barrel of confusing, so it may be worth consulting with one to save yourself a future headache!