I used 2020-02-13-raspbian-buster-lite.img because I had it laying around and wasn’t in the mood for another download. Installed the driver as per instructions and the display worked right away. Maybe the image you used is too new for the driver?
I soon found that the touch driver has no kernel support and that the way they activated the i2c bus on the display prevented the i2c_gpio alias from being created in the device tree, which makes it impossible to bind i2c devices’ kernel drivers to it.
I removed the i2c bus from the dts and recompiled, then set up the i2c bus using its own dtoverlay, which made i2c_gpio available in the device tree. The i2c bus uses sda=gpio10 scl=gpio11.
I’m now working on getting touch to work in X, which involves writing a kernel driver.
The rainbow screen will always appear on the external monitor, never on the HP. The HP is initialised much later and output then switches to it. It is very much like the corner-y hyperpixels there, it works the exact same way.