Your indicators will be different, but your actual O2 uptake should be essentially similar. Any difference should be due to technique (if you've optimized your breathing/rhythm/etc for one but not the other).

This is incorrect. VO2max is influenced mostly by muscle recruitment - different muscle group trained would be a hindrance if anything

"VO2max is influenced mostly by muscle recruitment"

This is incorrect - the primary factor is heart and lung function. Yes, muscle training can play a factor, but is relatively minor compared to that.

Lung capacity is genetic and heart is only trainable up to a small limit bc there’s a layer of fascia around it preventing further expansion. That’s the “supply” side of vo2. The “demand” side is the recruitment and efficiencies you’ve developed which are exercise dependent. This is why you dont see a lot of cross training (except for recovery) and a lot of z4 work in the professional training programs