I use RunGap to move all my Strava data over to Garmin Connect. So Nyon (bike.connect) (and also Peloton workouts) -> Strava -> RunGap -> Garmin Connect. It's pretty seamless and slightly annoying.
All the data gets moved over, map, hr, power, cadence, etc. It doesn't show rider power vs motor though - it only shows rider power which is all I want anyway...
I've been chasing perfectly connected exercise data since the early 2000s (IR connection from Polar watch to VidaOne on Palm phone right after workout, etc, etc). One day...