Normally
Window.softinput_mode
places a Kivy Textinput immediately above the keyboard:
But as I understand it the question is about the Webview example.
The contents of the Webview is an Android View rendering HTML (or similar), not a Kivy Textinput Widget.
So it seems unlikely that will work.
I have not tried it so I cant tell you what to do, but if I were you I'd try
android:fitsSystemWindows