Hi @benjamin.coenen,
Welcome to the Auth0 Community!
The Auth0 react library does not have this functionality as it would be insecure.
You should be issuing a set of client credentials as a new third-party application for each developer if you would like to provide your users with developer access to an API. We do not have an API key feature or direct equivalent.
If you search the forum there are topics discussing how to set this up. For example:
Hope this helps!
P.S. If you reply to your own topic it knocks it out of our unanswered queue and will often go unanswered.