I think they are inspired by something vaguely "Celtic", although they have not much, almost nothing, in common with real Irish or Gaelic Scottish or Welsh warriors of the period.
Irish/Scottish/Welsh clothing of the medieval ages is interestingly idiosyncratic, as many seemingly went barelegged (and with bare feet). That would have been a good opportunity to show some diversity in the game (where all clothing is of the same style everywhere), but the Battanians wear the same as the rest. Just with some tartan, that's boring. Maybe from the clothing they are modeled after Breton Celts (which did not use tartan however) from western France which were the least iconic Celts in my opinion however.
Celts of the time did not use much armor, by and large. Again, that's not anything near like the Battanians are (maybe understandable, for balance reasons). For the weapons, nothing especially Celtic. Why they have falxmen I don't know. The best is perhaps that they use some javelins, known as one common weapon in Ireland. The alleged focus on the bow reminds of the Welsh/Cymry who were famous for using bows and spears, albeit it is really weird to have nobles on foot with bows (I think there is no example for such a way to fight anywhere in any time of our history) and no normal archer line.
Calradia is fantasy and they can design the factions as they want, of course. It's just strange to bring partly some real world historical names into the game, and then mostly in wrong contexts.