There is no errata. There is no official answer. It either works in the way you change it at your table (maybe spirit damage with a trait, maybe spirit damage that only applies to enemies with the opposing trait, maybe spirit damage that only applies to things with a holy/Unholy weakness, off the top of my head) or it doesn't work.
Purely as a matter of personal druthers, going by how it seems most alignment damage effects came out of the remaster, the only option that makes sense to me is that this feat simply deals spirit damage.
It probably also should have the Sanctified trait so that a battle prayer to a holy deity excoriates demons etc, but since technically only certain classes ever gain sanctification, that might open a weird case scenario where a monk is speaking unsanctified battle prayers to Iomedae, who would require sanctification if the monk were able to do so.
Without regard for whether this is could cause confusion or unwanted knock-on effects down the line, I would allow a character who takes this feat to choose a sanctification available to them from their deity and treat Battle Prayer has having the appropriate trait--and obviously, their choice must match any existing sanctification they may have, if any.
This would cause Battle Prayer to run at my table how I feel like it should, and I don't think it ends up overpowered by any measure. Of course, I've already in the past allowed a cleric of a neutral deity to use 'divine' damage Battle Prayers and Divine Lances before the Remaster nixed alignment damage with no issues.
(EDIT: and mind you I've just realized that an Expert Religion feat allows anyone to create holy or unholy water if their deity allows sanctification, which even further lessens my hesitation to allow sanctified Battle Prayers)
Yes yet this is the internal guidance not a specific rule. We still don't know how to completely deal with these things that not yet adjusted to remaster.
Probably the currently most fair homebrew way to deal with it will be removing the alignment choose part, add a sanctification trait and do all alignment damage as spirit damage.
Given the guidance in RoE and how other things were replaced, it doing Spirit damage is the most sensible outcome anytime alignment damage shows up.
Now, is this one specifically supposed to be Sanctified or just base Spirit damage? There is no official answer, so your table will have to decide. To me, this one reads like it should be Sanctified given what you're actually doing.