SharePlay is not working...

So first things first, same thing is happening to me, I suspect it may be a hardware based limitation for individual is with older devices, but I will be testing that later today, second you need to report this through the FeedBack app on your eligible device which is enrolled i. the Developer Seed Program so that Apple is made aware of the issue as they do not browse the forums as much as the feedback app when they are looking for issues with their dev betas

SharePlay support in TV and Music and other SharePlay features such as screen sharing are not enabled in iOS 15 Beta 1, so this is expected. You are still be able to adopt SharePlay in your own app, and play around with the API in the interim!