Thanks for this feedback, which is at first surprising to me. This trail is officially recommend as hiking tour #17 in this guide: https://shop.kompass.de/shop/article/54445146/michael_will_kompass_wanderfuehrer_niedere_und_hohe_tatra_75_touren_mit_extra_tourenkarte.html (1st edition from 2021)

On the other hand there are many other unmarked trails around in the area of the national park, which are not tagged with 'access=no'. There is a long Wiki explanation about this tag: https://wiki.openstreetmap.org/wiki/Key:access

Following this explanation 'access=no' is very restrictive, meaning that "nobody may legally access" this trail. Such access restrictions should also be combined with an appropriate "signage" and "legal regulations". It seems to me that this does not apply here.