WHat does the green FaceTime button mean?

The green-colored Join button or the green camera icon indicates an ongoing FaceTime call. Hope this helps!

When I’m in a FaceTime call and someone else is viewing my message thread, like the screenshot above, can that person tell if I am on FaceTime? (Does the icon show green for them to let them know I’m in a ongoing call?)

How do I permanently disable this icon, I don’t want it in the same spot on my OLED TV and it’s intrusive. I’m not on a FT call and the icon keeps intermittently popping up, it’s so annoying. Tried disabling my continuity camera and I’m not on any FT calls. It’s still showing up.