They already specifically stated in interviews as well as here: https://worldofwarcraft.com/en-us/news/23090136/world-of-warcraft-classic-faq-what-you-need-to-know that yes, the BGs will be xrealm, so you don’t have to debate it.
Q: Will there be Cross Realm Battlegrounds when those go live?
A: Cross-realm battlegrounds were a feature of 1.12 and are important for matchmaking, so you’ll be seeing cross-realm battlegrounds in WoW Classic when Battlegrounds are introduced in Phase 3 of the content roll-out plan.