The app uses a NotificationListenerService to check for the presence of the "USB debugging connected" or "Wireless debugging connected" notification. When an ADB connection is detected this way, a WakeLock is acquired to prevent the screen from turning off. The WakeLock is released when the screen is manually turned off and re-acquired when the screen is turned back on.
The feature request (from 2016) to include this functionality in Android can be found here:
@Bubu I later learned there's already an app for it (doesn't support ADB-over-WiFi though):
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