There is an Android phone with 5.1.1 (Lollipop) version of Android.
In this system after installing Waze, it is still using its own VR (voice recognition) mechanism, (and not the Google Assistant one).
I'm perfectly fine with this, but now looking for a way for a 3rd party application to trigger the "Search by voice" function. Is this somehow achievable?
This one:

It's almost certainly using the Android SpeechRecognizer API rather than its own third-party solution. But, no, there's no way for other apps to trigger this voice search option. Not without some rooted phone madness that automatically opens the app and simulates the button presses or something.