I found and fixed the problem, and of course, it is the PSU. TL;DR: use a USB-C PD 2.0 power supply that can provide 35W for a single USB-C port.
I bought the Banana Pi M7 from this Amazon page, and the seller provides a power supply, with the board, that can only provide up to 20W of power. Even though the board specification says "Power Input: USB Type-C PD 2.0, 9V/2A, 12V/2A, 15V/2A", which implies that the board can require up to 30W of power. This caused most official images (Armbian and otherwise) to fail to boot. I happened to have a USB-C charger that can provide 35W of power, so I tried that instead, and it basically solved the whole problem. I tried multiple Armbian official images and they work as expected.
Thank you for your help! I hope this helps someone.
