Sorry it took so long to get back to you all. Here are my results for your suggestions:
As direct a connection to the pi as possible:
I excluded the ribbon cable and t-cobbler, but couldn’t skip the breadboard, as I don’t have any female-to-female jumper wires. Made no difference.
Apply 3.3V instead of 5V for power:
I connected the 3-5V pin to pin 1 (3.3V) on the Pi. Made no difference.
I thought it didn’t matter whether you use 3.3V or 5v, as the DC pin provides a reference voltage of 3.3V, and the power gets adjusted internally if necessary. Actually, I started out with 3.3V and switched to 5V when the screen didn’t respond. I hoped a bit more ‘oomph’ might help. It didn’t.
Check the back for contrast adjusters:
I didn’t find any. It does have a ribbon connector, but it seems fine. I decided not to touch it, as my fine motor skills are not what they used to be.
Edit: I’ve just tried looking at it through polarised lenses, and different examples (gif.py, image.py). Rechecked everything suggested in this thread, just in case I missed anything. So far, no luck.