Is there a function built into macOS that will allow me to freeze an external monitor?

Is it possible, natively or with a software, to allow a mac that is mirroring onto an external display to freeze that display so that the macbook may change scenes and then unfreeze the frame.

For context: I have a mac that is connected to a TV for external use. From where the macbook user is positioned they cannot see the TV so it is easier to mirror the macbook rather than setting it as an external/additional display. However, there are some instances where the person running the macbook will need to change applications or do things behind the scenes and therefore temporarily freeze the TV on whatever the current screen is and then unfreeze it when they are done. I am looking to be able to freeze the screen rather than simply unplugging it and having the screen turn black. Also, I am pretty confident that this would be able to be done with OBS but OBS is pretty taxing on a computer and I was hoping that there would be an easier way to do it.

I have an option of using different macbooks. All of them are currently on the most recent version of sonoma, and ones that have the M1 chip, M2 chip, and the old i9 chip.

[Re-Titled by Moderator]