Not exactly: is described on wiki but it is in "proposal draft" status, as you can see:
https://wiki.openstreetmap.org/wiki/Proposal:Via_ferrata#Tagging_as_route=via_ferrata_relation.

The tag used on "way" is different because is official, see:
https://wiki.openstreetmap.org/wiki/Key%3Avia_ferrata_scale

Also usage statistics on OSM the tag on "way" is much more used, see:
https://taginfo.openstreetmap.org/keys/via_ferrata_scale#overview

Furthermore, a via ferrata very often has different difficulty levels that can be set on the "way", similarly to the sac_scale tag