Jay & Others,
I'm afraid that my proclamation regarding the solution to the above mentioned bug by executing the line of code:
CurrentValue[$FrontEnd, {RenderingOptions, "PreferredGPU"}] = "GPU"
was a bit premature. Unfortunately after running several notebooks with dynamic functions (Manipulate and ListAnimate) the problem arose again even after executing this line of code.
Nevertheless, by setting it equal to "GPU", all of my graphics /plots do now work/render significantly faster. Unfortunately the self-test/unresponsive kernel issue wasn't resolved. This did, at least, force Mathematica to utilize my Nvidia GPU for graphics rendering. Incidentally, when I set it equal to "Software" as suggested by tech support my graphics rendering slowed. I believe that you need to have a Nvidia GPU installed locally on you computer.
Jay, did you try setting it equal to "GPU", or to any of the other options that you listed? I didn't know what the valid options for this instruction were, I just tried "GPU" and it accepted this input. I knew that, with regard to Mathematica's GPU computing and deep learning functionalities, "GPU" is a valid response for some of those related instructions and so I just tried using "GPU" in this case as well. I would just try each of those that you listed and also "GPU". There is no harm in trying them since you can easily revert back to "Automatic".
I did send a follow-up note to tech support inquiring about the availability of version 12.3.1. I'm expecting a response back early in upcoming week.
Regards.