Actually, I got it working. Turns out the 3V pin wasn't enough power for the screen. I put it on the 5V and it worked fine.
I just discovered another issue, unrelated to the screen, as I tested it with the screen disconnected.
I have the RP2040zero plugged into a Adafruit 5999 USB hub. From that, I have a PS5 controller plugged into port 1, and a thumb drive plugged into port 2. If I then plug a Dreamcast controller into another port of the console, the entire thing dies; controller doesn't work and memory card disappears. When I unplug the Dreamcast controller, it comes back (sometimes it doesn't come back until I restart the console). If I remove the thumb drive, and just have the PS5 controller plugged into port 1, this issue does not occur.
This issue only occurs if a thumb drive is plugged in.