I haven't tested with an Android emulator in a long time, but as far as I know the database import/export should work the same was as on an Android device. Does your emulator include filesystem access? If not, then it won't work.
Windows 11 is supposed to have native support for running Android apps, but I don't think that feature has been released yet. Also, it will require buying the app again from the Amazon app store, assuming you originally bought it from the Google store.
Another option is to switch to BandHelper, which includes a web interface for managing your data from a computer:
https://www.bandhelper.com/main/SLM_comparison.html