AR would be more specific but contrary to what others may say XR would also work and technically does cover the whole enchilada. Your team is working on a way to also enjoy passthrough videos with virtual backgrounds, if that's not the whole enchilada right there, then I don't know what is hahaha
I guess saying XR is like saying human instead of american, asian, or african I guess. It's a broader category that cover multiple sub categories within it, why would you not be able to use it? I guess I would personally and maybe for financial and market saturation purposes see which term, other than VR is more widely used and popular with the masses. That way you can decide if you want to get more specific with AR or more broad with XR.
XR to me just sounds cooler but I have to admit that AR to me sounds more familiar and widely used, specially by people who are not super into this stuff like we are. My wife for example, she is more likely to know what AR is vs XR if I ask her if she knows what either mean.