I'm not able to get this to work with gestures enabled on my phone as it just engages the back gesture which closes the app. It does work with gestures turned off though.

It seems like the back gesture should open the menu instead of closing the app. If you're editing a note, going back exits edit mode, then back again shows the list of notes in the current notebook, then back again should open the menu to show your notebooks. Or if it was easier to swipe to open the menu without engaging the back gesture that may be a good solution as well.