Hi Eliklein02,
The screenshot in the article below shows the participant on the call at the bottom right corner of the video screen.
Share your screen in a FaceTime call on iPhone - iPhone User Guide
"In iOS 15.1, SharePlay lets you share your screen in a FaceTime call—you can bring apps, webpages, and more into the conversation. You can show off a photo album, plan your next vacation together, or get feedback on something you’re working on, all while seeing and hearing the reactions of others on the call."

It might be helpful for you to speak with an AppleCare technical advisor about this issue. Click the link below, choose the phone number for your region from the list, and call when it is convenient.
Contact Apple for support and service
Take care.