Looking through the comments, I can't imagine how else it could possibly be explained or clarified further. For this use case, it is assumed that the software producing the visuals has full control over the output. An orange dot that cannot be removed means that the software does not have full control over the output, which is unacceptable. It's that simple.
EDIT: As far as I know, the best long-term answer here is for apps that present visuals full screen to "capture" the external display for exclusive use using an API (https://developer.apple.com/documentation/coregraphics/14562...), but that's not super common right now.
Sounds like it's totally possible for the software to have full control over the output if it wants to, this only affects software that runs in a "standard" fullscreen mode without explicitly taking full control over the output.
Sounds like it's totally possible for the software to have full control
Yes, so you can go to the software vendor's "Ideas" or "Suggestions" page and ask for this, and post in forums asking people to upvote it, and hope the devs will do it. Not a great workaround. And sure, someone developed a script to get rid of this but no one is all that happy when Windows does something user-unfriendly that only a regedit hack will get rid of either.