To Javier, who wrote on Mar 31, 2022:
"I just changed it in settings. Or go to help and write wallpaper. Changing the wallpaper takes away all the purple goes away. Oh, I got it. You have to go to "Desktrop and screensaver" in your settings. There you can choose amongst a bunch of looks."
That's not actually what the question here is about, unfortunately. The semantics of this are a bit annoying/awkward, but it comes down to the difference between LOGIN SCREEN and LOCK SCREEN.
When you change your desktop background in the Desktop & Screensaver settings, the desktop background you choose will by default carry over to the LOCK SCREEN, which you see if you remain logged in but either lock the computer manually or let it lock automatically [after whatever amount of time it is set for in System Preferences>Security & Privacy>General].
The question here is about the LOGIN SCREEN, which appears when the computer is first started. Somebody mentioned here that you should see the same login screen if you simply log out (without shutting down the computer). That doesn't appear to be the case on my computer. If I just log out, I do briefly see the default colorful LOGIN SCREEN for a second or two, but then it switches to my LOCK SCREEN (which I currently have set to just a solid black).
I think I've tried all of the suggestions offered in this thread and in every other forum I can find where this is being discussed, and none of the suggestions offered appear to make a difference on EITHER my LOGIN screen OR my LOCK screen.
So I'll continue to search and submit this feature request to Apple, because I also really hate the startup login screen (and even worse, I hate just not having control over it). :\