ELI5: How can I protect (a bit) against this BMC issue?
This might give some comfort since you can load your own firmware, and then compare that is indeed what you are running, and then have it diagnose itself for other injection points.
Another approach you could take, you could create a small widget that would connect to the JTAG, I2C, SPI chains, and read out all code and compare it to expected checksum, holding the power-off line until you are finished. Imagine maybe a small ESP32-class device that has a GPIO that goes to the ATX PS_ON# line, and each JTAG/SPI/I2C. When power tries to come up, you scan, and if all match, release the PS_ON#.
The article Lee linked is quite good.