Altitude correction and course

Freddy said:

So what is the real positive elevation for this course ?

"Real elevation gain" does not exist :-). There is no standard for that. It depends very much on the resolution. If you start counting the height of every pebble you step or ride on, the elevation gain may grow by orders of magnitude. In cartography, this problem is known under the name the Coastline paradox - Wikipedia. However, as long as the GPS track looks accurate, I'd trust more the Total Ascent value in the activity stats, since the Course may be optimized beyond recognition.

Freddy said:

So what is the real positive elevation for this course ? + 1404 m or + 1944 m ?

Freddy said:

My watch registered 15404 m of positiv elevation.

I still think that the REAL problem seems to be the altimeter on your watch not working properly.

It is normally not absolutely necessary to use the elevation correction. The barometric altimeter data usually works better than GPS when used correctly.

Freddy said:

My barometric altimeter is broken on my watch. That's common on Garmin watch

I can't confirm that. I have been using the various Garmin watches since 2016. So far, I have only had one device that had incorrect altitude and barometric pressure values due to a hardware defect. I cannot say whether it was the baro sensor or the temperature sensor. The replacement device works well.

If you are unable to rectify the fault yourself, I suggest that you contact Garmin Support to have the device replaced.
just my two cents.