Inspiration tells me that we should look at clause 151, which refers to a relevant Welsh authority, whose functions

“are exercisable only in or as regards Wales, and...wholly or mainly devolved Welsh functions” and a cross-border Welsh authority, which is not one of the above and has functions that are exercisable

“in or as regards Wales, and...is a devolved Welsh function.”

That seems to suggest that being a devolved Welsh function makes something into a cross-border Welsh authority, if indeed it is cross-border, because that is presumably a key requirement.