The Stack Exchange app is well-built as far as apps go, and I enjoy using it to participate. Out of curiosity, does activity on the app count towards consecutive log-ons for badges?
Yes it does. This was addressed on Meta Stack Exchange a few years ago, and is now working.
My experience confirms what the answer says on that page – I have kept my streak alive on this and other SE sites by using the Android app. But, it's not sufficient to simply open the app – I have found that it's necessary to actually load a new page each day, otherwise it won't register.