this would be the web-based way to do what is described in the post that you referenced above: https://forum.inaturalist.org/t/how-to-create-new-places-with-the-help-of-openstreetmap/6701/5. hopefully it’s relatively straightforward. if you have questions, feel free to ask.
UPDATE: i forgot to mention that you should check to make sure the place you intend to add doesn’t already exist in iNat. in the case of the park that you referenced in your original post, it looks like there’s already a version of the place in iNat: https://www.inaturalist.org/places/bukki.
just a guess, but if you export directly from OSM (without doing some transformations via the Overpass API), you’re often exporting points or lines or some combination of features, rather than a polygon. so if you try to import non-polygon features into iNat, iNat won’t like that.