Most of the time, elevation data comes from the watch and thus from GPS. And data in the Stryd app is from most of the time GPS. Only Stryd app on the Apple watch and the Stryd app on the phone will record Stryd elevation.
Since elevation from GPS is not very accurate, both Garmin and Strava do not simply read elevation data but manipulate the data to be more accurate (for example, Strava will map horizontal GPS data onto a map to correct elevation data). Stryd simply calculates elevation gain based on the FIT file without correction. Hence, you will find differences in elevation gain in various platforms.
For additional information, please contact firstname.lastname@example.org.