I don't know of any device that has continual sync with third party apps. No point really. The usual process using such apps - Strava, RWGPS or Kamoots, is you are developing a navigable route on those websites, then downloading that route to the device. You then use the device to do 2 things, 1) Follow the navigable route created on the website and using turn-by-turn as well as map cues. 2) Tracking where you ride. When you compete a ride, you then save the ride, it typically then uploads the completed route to the website for the particular device you are using (Garmin, Wahoo or Hammerhead), which then ports that completed activity onward to the activity tracker you have chosen - Strava, RWGPS or Kamoots.
Most of these devices allow re-routing should you encounter a detour, go off course, etc... some better then others. Garmin can suck at it. Karoo 2 is a bit better, I've no idea what Wahoo does. One major issue you run into with re-routing is you are now relying on the device to calculate a useful route to get back on the course. How they do this is an issue as they just are not that smart and sometimes the recommended re-route just is useless. Often times you are better not following the device re-route, just look at the map and follow your own. This is one reason touchscreen devices that have large screens can be more useful as it allows you to zoom and pan, plus there's more info on a small screen.