changing the master password should be through the application itself, without the need of the webpage
It will be much better
I disagree with this. I like forcing the person to go to the online vault and re-authenticate before being able to change the master password.
You could deliver that workflow through the app, but it would feel a bit more clunky in my opinion.
Just remember that there’s a certain amount of people that browses and do their jobs only via smartphones.