This is my real world advice from someone who travels often.
Regarding traveling with drone batteries: It's not as scary as everyone leads on. Lots of other electronics use LiPO. Your drone is nothing more than a moving camera not contraband.
Carry all your gear onto the plane just as you would with any other piece of electronic gear/camera gear. Various people pack various ways. I usually put all my drone gear in a camera/dslr bag with my other equipment. Or I bring a minimalist style case for my drone. For my
air2s I have a PGYTech one that fits all my accessories as well as my drone and I slide that in my carryon bag or backpack.
It it was me and as someone that has and does travel internationally often I usually...
A. read up on laws/rules of where I am traveling. It that is a bit confusing I then
B. Look on social media for drone groups or the places I am traveling. Usually people who live in these places have the best answers on where to fly, where it's frowned upon etc.
Then sometimes I
C. Search for YouTube drone videos of those locations. I will sometimes message or comment with my questions on the creators page. Usually I get my questions answered and sometimes I don't.
I find it much better and I get better piece of mind from people with actual experience flying in these places vs someone who just copy pasted something from a various website.