After adding the Family Safety section to the new Edge browser on desktop, Microsoft is now rolling out Family Safety features to the Edge browser on Android.
Back in February, Microsoft has added Tracking Prevention, Contextual Search and favorites and passwords syncing to Edge on Android, recently the company pushed an update to Edge Android version that allows parents to monitor their kids’ web activity, block certain websites and apps and set screen limits and access other family safety features when they sign into Edge with their Microsoft Family Account.

Updating Edge by visiting Play Store and checking “about this app” in Settings not only tells you Edge App version info but also reveals whether all family Safety features are rolled out to your device or not.
Edge 45.03.4.4944 changelog:
1. Sign in with a Microsoft Family account to get real-time web activity reporting, content filtering, and other secure features to help kids safe on mobile.
2. We’ve also made some general bug fixes and performance improvements.
Related articles:
Microsoft Chromium Edge adds Family Safety to its Settings
Microsoft Edge Canary gets Microsoft Family Safety Support
Fix “We Couldn’t connect to Microsoft Family right now” error in Windows 10 1903
Microsoft Edge for Android rolls out Tracking Prevention and Contextual Search features