As pointed here there is a technical problem running QS v2 in a local environment, which is a current use case for the Very Small GLAM configuration of Wikibase Suite.

In the words of @ACorrea-WMB:

I'm currently improving the local deployment actually, but you can try it out already, check the docker-compose file
to run it locally, we use an owner-only OAuth token
basically just using what sould be sent in the Auth: header
its the "developer login"

At this moment I really don't know how this should be done, but hope I will in next July.