Update: I went to my Genius Bar appointment and, due to the many issues I was already experiencing aside from the screen flicker/battery drain - including a crash while doing a screen recording in Quicktime, my camera being ridiculously grainy, and more - he said that I might need a new display, a new logic board, and a new battery. He suggested that I needed to send it in for repair.
After thinking about that a bit, I realized that if I needed all of that - and all of that was replaced - I would be given back a refurbished MacBook, which is not what I paid for a month ago. I paid for a new computer. So, when I went in to drop it off, I asked to talk to a manager. He was super nice and suggested they triage it at the store instead of sending it in, and said he would "make it right" if this didn't fix it.
So, I left it there. They ended up running hardware checks (which the Genius Bar guy already did) and then said that they would like to erase the computer and see if that helped. They were also supposed to run a whole bunch of tests to replicate the issues I was having. I told them to erase it and go forward.
They called me a day later and told me that I could pick it up. I get home with it and realize that all my Mac apps have now been erased completely and not restored - so Pages, Numbers, Garageband, and Keynote - all of which are what allows the computer to be used as a computer and are all things I use in my work. I was SUPER annoyed, because that also meant that they could not have attempted to replicate any of my issues, as they would require that someone was doing a Keynote while doing a screen recording while using the camera to do a movie recording (which caused a horrible WHOOOOOSH sound and then crashed).
Not cool.
I called the store and someone in repair told me that there was "no one in the store that could help me" and he "would refer me to Apple Care." I tried to explain that they were the ones that did this AT THE STORE, but he transferred me before I could even explain that. Really not cool.
So, I ended up chatting with another Apple Care Advisor who finally upgraded me to have a senior advisor call me. He was super nice and told me that my issues should be resolved by upgrading to Catalina. So, I just did that. Nope. Screen flicker came back literally one minute after rebooting. Once again, I turned off the automatic graphic switching, and, once again, my screen flicker stops but my battery drains at an astonishing rate. As in, it's been 35 minutes since I turned that off, and my battery is down to 78% from 100%.
That's obviously not a solution for a portable computer. I am not lugging my charging cord with me everywhere just so I don't have an annoying screen flicker every 15 to 60 seconds.
I've got a case number from the senior advisor, so I am going to try this again.
I've seen people saying that a NVRAM reset and a SMC reset may fix this issue. I am going to try that tomorrow and I will report back if that helps.
This is costing me a ridiculous amount of time to try to sort out on a new computer, but here we are.