I think I would like the have the same feature as suggested as, though for my purposes, your suggestions of new notes & search are a bit too specific (but I see their merits), since my issue is on which vault to add a note/search in.
For me, the following would be desirable: On the main Android screen, if I long press on the obsidian Icon, there should be a pop-up showing available vaults, so one can choose which one should be opened. I use separate vaults for personal and private info. Switching in between these two within the app is a bit cumbersome and of course, the one I need is never the one that opens.
A workable alternative for my interpretation of this feature request would be: Pick vault on app launch