What is the recommended way to handle common strings and dimensions? Should we store them inside .xml or should we have them as global variables?

It’s still Android, all of these have a reason to exist like strings and how they make having the app in different languages easy. Global variables sounds like you’d be re-inventing the wheel when you need to solve those same problems.

I agree 100%, but it's interesting to think through what this looks like for Compose multi platform? Is there any natural abstraction for this?

Having the composables still receive the text as strings but resolving it higher up in a platform-specific place is the first thing that comes to mind. Otherwise not aware of any library that abstracts this out.