I'm not overly paranoid or anything, but the thought of my seed phrase playing peekaboo with security personnel during a manual check doesn't sit right with me. Do those X-ray machines get nosy enough to pry into my steelwallet's secrets, or am I just overthinking this?
There's no way to see the phrase with x-ray inside your bag. All they'll see is a metal object, round or flat, depending on what type of a seed storage device you have. The problem is that they might think a steel container is some kind of a weapon.

Something like this in your bag looks a bit like a small explosive device (IED), but they won't take it from you (most likely) just ask you to show it and unscrew the cover. They won't see each individual seed, but if you're scared about exposint yourself as a bitcoiner, better travel with a paper wallet.