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.