You get people to adopt technology or paradigms by explaining the benefits and drawbacks of adopting that set of technology/paradigm and then discussing it together with your team/s. Not sure why it would be different for Statecharts compared to any other paradigm?

What process is too hard for you now exactly, to describe states or something? You're already doing this implicitly when you write UI code with state. Statecharts only changes it from being implicit to being explicit. If you're having a hard time actually naming your states, you can use tools like https://sketch.systems/ to explore what you're building with a simple DSL, then implement it properly in the programming language of your choice.