The bringup module always boot which configures the clock controller, bootguard parameters, and releases the CPU core from reset. When in HAP mode, after that it only handles power management events and doesn't really do anything else. No other ring 3 processes are started on the ME in this mode.
Stuff like even the real read-write VFS, fw updater, HECI comms handerl, AMT, PAVP, ISH server, etc are never started in HAP mode. It effectively reduces your runtime attack vector to data in SPI flash only.
As mentioned in one of the linked tweets, ME was possible to exploit through early-boot attacks before the HAP bit was even checked. So non-negligible things happen while it "boots".
While they are genuine vulernabilties, I wouldn't consider this a worse problem than being able to inject rootkits into other parts of the firmware which is also the case here.
And the understanding that we have is mostly limited to what is in flash memory, e.g. the ME's BootROM hasn't been dumped yet (as far as I am aware).