Could anyone confirm whether RAW, there is an internal order within each phase? For example, in BX D&D combat plays out in the order Movements, Missile, Spells, Melee. Then the next group in initiative order goes down the same sequence.

I'm not sure I could find a corresponding quote from the rulebook concerning Combat Sequence. But Talanian made a comment here. I wasn't sure if the comment was relevant to the current AS&SH 2e.
odd74.proboards.com/post/111930/thread
"There is no internal order within each phase; it's a little more abstract in that sense. So, while the phases themselves are ordered as you note, there is no specific order between melee, magic, missiles, and movement. "

My reading is that during each phase the initiative winner can perform any of the action types and then the next group in initiative order can perform any of the sequence in any order.