Does "Draw over other apps" permission allow the app the see the content of the background app? For example, if I have the messenger bubble open in the foreground and I am browsing through my photos in the background, can the app like messenger see the photos in the background and record this data? not only messenger but other apps that have this permission.
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.