After pairing a Stryd device with the COROS watch, you need to add running power to the data screen of your COROS watch to be able to see Stryd power while running and to make sure that your watch records all the Stryd data.
COROS can show real-time, (Running Power), average, lap average, 3s average, 10s average, and 30s average. You can have as many power data fields as you like, and you can combine power with any other metric provided by COROS.
You need to use the COROS app to change the data fields on your COROS watch. Open up the app, select the device page > workout data > run (repeat for trail run, etc. as applicable) > page > change metric (see below):