Ability to use data from geodaten.graz.at

So, the current state of what we know is allowed can be found at Contributors - OpenStreetMap Wiki

Theoratically there is https://www.data.gv.at/ - an open data initiative but unfortunately its ‘just’ CC-BY 4.0 without an special permit for OSM and its not sure they are willing to do issue one.
There is hope - OGD - Dual Licencing am Horizont - but until then CC BY 4.0 can not be used.

What you can do is ask the Ansprechpartnerinnen at Online Karte: Baumkataster - Stadtportal der Landeshauptstadt Graz if they are willing to issue a special permit/waiver for OSM. Information about this can be found Use of CC BY 4.0 licensed data in OpenStreetMap | OpenStreetMap Blog here and the waivers can be found Licence/Waiver and Permission Templates - OpenStreetMap Foundation here. You can also look at the last one in austria from “Government regulator for electricity and natural gas”.