What’s my best option if I want to write an online book in this style but from an IPad? It seems like I’m stuck using something like Ulysses and the setting up a tool chain on a VPS or something... anyone have any tips?
Not sure what's Ulysses, but you could probably set a Github action for it? This way it would be rebuilt and deployed on pushing into your git repository (hopefully it's possible to work with git from an ipad?)
It is possible to work with git from an iPad. I've set up a similar workflow (not for mdBook but for gitbook) a long time ago. I used Working Copy and Textastic.