I have not seen an indication of why this matters, however I suspect that it is because Garmin is doing something different when it transfers the data - when I complete a workout on my Garmin the activity shows up in Garmin Connect automatically with the TR workout name appended. So there must be something else that TR is looking for in the Garmin sync which enables it to see the completed workout properly. That’s lost in the sync to Strava. This would also explain partly why workouts done on a Wahoo don’t work - Garmin must be doing something extra at the workout sync stage.
Mine says “Power Source Garmin Edge 810” - but I think that’s just a record of the device. At the bottom of the page I see this: