It’s probably based off of a barometer in a watch, not GPS, and the air pressure was changing

Yes, a high-pressure area was moving over Italy the last couple of days.

The elevation in this case is just a proxy for storing the barometric pressure, which is because the actual air pressure is the important thing to track if you are trying to normalize against athletic performance. If the watch logged the GPS altitude, it would be a lot more accurate, but less useful as the air density would only be estimated..

All GPS watches already calculate their altitude (GPS uses three dimensional trilateration for computing the position, so you must get the elevation because you must calculate the three dimensional position). The elevation measure is usually pretty inaccurate in Central Europe. Since the satellites are comparably low above the horizon, flat movements of the runner have a large effect on the run time of the signals coming from the satellites, while vertical movements do not really change the run time and are therefore much more affected by any error.

This is why most portals like Strava run a data correction by overriding the elevation data of the GPS track by tracing the path over their internal elevation model.

The barometric elevation calculation is usually much more accurate and is constantly calibrated on the watch. This breaks down a little if you run for over 24 hours and the weather changes a lot. The drift over the 24 hours of this run amounts to about 8m over 2 hours, which doesn't really matter. And while air pressure can be used to normalize performance of the athletes, the absolute values measured by the barometer are usually pretty inaccurate, while the relative changes are quite accurate. Therefore, they can be used to measure climb/descent, but not really for an absolute air density measurement.

Source: I have worked on a GPS wearable (without barometric pressure sensor).