PS: for safety, it might be worthwhile to adapt the plugin to consider this custom upload folder setting possibility
@hardeepasrani, thanks for your help and finding the “strange different upload folder”; googling a bit I found an apparently “ancient WordPress configuration setting”:
https://imgur.com/a/iBqyl1K
After I put that field “blank” and saved the setting, the problem was, not only solved, but that setting option disappeared all together from the dashboard. So it seems this was an ancient WordPress setting that has since been dropped and was causing this issue. So if anyone has identical problem as me in an old WordPress installation (my first install was in year 2007) one just needs to put that custom upload field blank and save settings.
Thank you!!