Sorry about that, you are entirely correct.

The path is recent and only intended to be used on foot, for exercise (https://www.bruzz.be/stedenbouw/nieuwe-finse-piste-park-thurn-taxis-2021-05-03). I should probably add "wheelchair=no", as there are a couple of steps and the surface type is generally not suitable for wheelchairs.
Once the track appears on the aerial imagery, I will use that to improve the accuracy where necessary.

Sounds good, thanks! Any thoughts on the choice between footpath and track? To indicate the difference with the other paths in the park, I would favour track.

It is not signposted and I don't think it is an official road name according to the city. There are similar tracks in Flanders, which are also not signposted but are nevertheless marked with "Finse piste" on OSM. I have not been able to find an equivalent term in French, but it seemed inappropriate to only add a Dutch name. I'm not sure the name should be visible on the map, but it would certainly be nice to be able to find it when searching for this term. Other Finse pistes on OSM are marked path, track or footpath. Perhaps track would be better than footpath here.

You are correct (https://www.he-ferrer.eu/haute-ecole/implantations), I re-added the amenity tag.

Changeset comment incorrect, should be: marked town hall