Fix expert mode start button loading state

[binhmod]

Previously, the loading state was shared across all start options
(Root, Shizuku, ADB), causing multiple start buttons to display a
loading indicator simultaneously.

This PR scopes the loading state to the selected start method by
checking startingMethod, ensuring that only the active start option
shows a loading indicator. The loading state is also cleared correctly
once the system bridge connects.

Translated from Vietnamese to English using Google Translate. Thank you.

[juangarcia15894-a11y]

Buena

[sds100]

All buttons need to show the loading indicator (or at least be disabled) because you shouldn't be able to start expert mode with root while you're starting it with shizuku for example.

What do you think? Thanks for contributing though :)