In the camera - no issue Out of the camera - with the orange cap on Never never loose, so that the terminals could short out each other, potentially causing a fire
In real life, although I only fly a few times a year, I've never had an issue or question about the two or three spare batteries I almost always carry in my back pack. I've been dinged on my rescue inhaler more than anything else!
Here is a link to USPS rules for lithium batteries, which assume that your package will go by air. Very similar to TSA rules. When I was involved with shipping, these are the rules I used. Kinda long and technical if you're interested.
Leave them in the camera and carry it on. Donβt put it in checked luggage. Of Course very few people would even think of packing the camera in their luggage. Too much chance it might go missing.