The point is, battalions don't have faction keywords anymore - I'm looking at the Nighthaunt battalions as I type, no keywords. And in the core book, all I can find is "If a player's army includes the units needed to field a warscroll battalion, then the player can include the battalion as part of their army by paying the points cost for it as shown on its Pitched Battle profile." I suppose its listed under the Nighthaunt pitched battle profile, but as far as I can tell the rules themselves seem to let you mix and match as you want.
This is also addressed in the FAQ:
Quote
Q: Some warscroll battalions included in battletomes do not have a faction listed above their title. How do I determine which faction they belong to for the purposes of allegiance abilities?
A: The battalion belongs to the battletome’s faction. For example, the warscroll battalions in Battletome: Stormcast Eternals are part of the Stormcast Eternals faction.
AoS 2 - Legion of Grief discussion
in Death
Posted
This is also addressed in the FAQ: