My first thought is that’s a windows related problem. Depending on your specific windows edition, it is not possible to log in multiple accounts at the same time. Microsoft earns a lot of money for this feature as they get paid for user- or computer-CALs, which are licenses that allow an amount of users or machines to access a single so called terminal server. Correct me if I am wrong, but the sunshine/moonlight setup seems to use RDP (never actually checked on that, because I was just happy that it works). So if that’s the case, then there unfortunately is no easy solution for your idea.
Also look here:
https://www.thewindowsclub.com/enable-rdp-for-multiple-users-on-windows-11