Unable to Share Screen on Facetime with iPhone 15 Pro

Hi everyone,
Ever since I received my iPhone 15 Pro, I have been unable to locate the Share Content button while on Facetime. I'm assuming this is because the Facetime controls are in the dynamic island, but even when I go to the app switcher and bring the controls up there, the button doesn't show. I know that this has nothing to do with iOS 17 specifically, because this worked just fine on my old 12 pro running said OS.
So, if you've got an iPhone 15, or even 14, as I'm wondering if it's due to the dynamic island, are you able to share your screen with people, and how?
I should clarify that I'm trying to watch things like YouTube with people, and not just Apple-specific apps. There is the shareplay button up there, but when pressed, it brings up a seriously broken screen with unlabeled buttons using VoiceOver. I'm seeking the share content button, where you can select "Share my screen".
Any tips or ideas on how to do this would be much appreciated.