Does "Draw over other apps" permission allow the app the see the content of the background app?
The official developer docs do not mention any such possibility with Draw over other app (SYSTEM_ALERT_WINDOW) permission. Apps with that permission can only receive touch feedback, like other apps. 

See:


TYPE_APPLICATION_OVERLAY
ACTION_MANAGE_OVERLAY_PERMISSION
SYSTEM_ALERT_WINDOW


However, any app with Accessibility Service enabled can read the content of the active window.