Finally had a chance to fly with it. I was able to pack all my usual stuff in the backpack - chargers, 14" MacBook Pro, power bank, other small items, and even AirPods Pro Max, in addition to AVP in Eucarlos case.
I put AVP with the lens cover on, the battery, additional light seal cushion (W+) and AirTag.
I used a soft lens protector (kiwi) from Amazon just in case, and left my inserts in the AVP.
The case did its job well, however one of the zipper handles broke off as it's made out of cheap plastic. It even fit into a hotel room safe, which is a plus!
Using the AVP on airplane is a pretty good experience overall, but has definitely more friction to start using than an iPad or MacBook, so I'd probably not even bother on short (<2 hours) flights.