Depends on how you define "booting". While its true that the microkernel always boots, and there is one userspace process running, it's a bit more subtle than that imo.
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".
Absolutely is, one of those exact attacks is being used here to bypass BootGaurd. However all pre-boot attacks I am aware of rely on writing a malicious payload to the system's SPI flash and involve physical access.
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.
In my understanding, the concern is not what outside attackers can do. It is what capabilities exist under Intel's control before they are reduced to some hopefully benign subset.
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).
...Dell? I have multiple of their machines which have been configured via their B2B panel to have ME fully disabled.