I have checked to ensure my bluetooth is only connected to a single controller so there is no influence from other devices. I have used DS4Windows emulator and it does not fix the issue.
I have checked and ensured the controllers are being seen as Controller 1.
Steam recognizes the controllers and I can use them in other Steam games. The XBOX controller was used on another computer and was able to play Stardew Valley from the other computer. I have individually attempted to used both a PS4 and an XBOX 360 controller (not at the same time) with and without cables and they do not work in Stardew Valley.