Oh! I actually can personally answer this one. I’ve been a competitive air gun and rimfire .22 LR for years and even attended college on a rifle program scholarship at a D1 program (yes! The US has a major collegiate rifle program)
Traveling internationally depended much on where you were going. We competed at the international junior Olympic championships just outside of London one year in the UK. We had to package all ammo and firearms separately, in locked containers which ultimately wasn’t that big a deal. As with flying with firearms in the US, it ultimately comes down to how familiar those such as gate agents and check-in staff are at the airport with their country’s firearm travel laws. Flying out of the US was always easy as they’re used to firearms, but flying back to the US was sometimes a nightmare and we’d get to the airport up to 6 hours before a flight to deal with any BS.