“onsen tamago” is just a name for a boiling style, it is rarely done in an onsen water, many restaurants will propose it.
Another popular one is the “perfect egg” with a solid white but a liquid yolk (my favorite!)
Where I was living “omelette” was a word for the runny kind, but the well cooked one (much more common) is tamagoyaki
I was invited once in a nice traditional onsen and at one point realized that between the polished stones and the bamboo pipes fed directly by hot springs, the raw fish and the rice served in traditional pottery, I was enjoying a luxury vacation in a place using mostly prehistoric tech. That changed my view (a bit) on tech paths.
If only we had kept our population low enough to only live in places where life is particularly easy, well… life would be particularly easy!