Add another attempt to check write permissions on a folder (fixes #1971)

[wrobbins]

Description

Fixes issue https://github.com/syncthing/syncthing-android/issues/1971

Changes

• Add another attempt to check write permissions on a folder translating ~ to externalStorageDirectory.
  • ignores Constants.PREF_USE_ROOT
  • uses java.io.File to check access instead of shelling out.

Notes

This an unobtrusive change, leaving the existing write-access check in place.

I tested this on a Pixel 6 Pro with Android 14.