Correct. I disconnected the monitor, shut down the computer, restarted the computer and it does not happen when I use the MacBook alone.
Right now in "Displays" I have the LG Full HD set for "Main Display" and the computer has the wallpaper displayed and I have no issue with the purple screen on either device.
I'm okay with the computer showing the wallpaper as long as I can use my monitor. And there is no issue if I'm only using the computer. Whew. What a journey. Luis, thank you for your help. Your questions helped me think about the issue and try different things and come to a resolution that I can live with. But I do think it's interesting that this only happened after I updated to Sonoma 14.7.4 and continued after I updated the firmware on the monitor. Even though I updated the LG firmware, I think there is an issue with Stage Manager and LG's On Screen Control if I use the monitor as "Mirror for Built-in Display". Thanks.