Unfortunately, it's a framework. That is, it demands to own the event loop.
It has a type "Application" (This is Rust, don't get to say "it has a class Application, which you subclass", but that's how it works.)
That's fine for a cold start where you do everything their way, but tough
if there's already an event loop. egui, in contrast, is just a library crate which needs to be called on each frame.