On the app... quite possibly depends on the type of phone & OS version + available phone memory & battery saving settings.

My Samsung with Android 7 couldn't do this. It could only remember the last opened layer + forecast model for a short while, maybe a few minutes after closing the app. But after a longer time, it would always open on Wind + ECMWF (which is the default settings on Windy)... However, after upgrading the OS to Android 8 Oreo, my phone seems to always remember the last opened layer + forecast model.

EDIT: After some very long while (didn't get the chance to measure the exact value; let's say just after the night as I am opening the app so often during the day :)), my Android app does open on Wind + ECMWF.

Forgot to mention that I'm a beta-tester (version 16.12.3 at the moment)... But my friend's regular Android app always opens on Wind + ECMWF by default.