You won’t be able to access the webtask storage associated with the extension as that is private to the webtask running the extension. That extension in particular allows to be configured in a way that the user data (groups, roles, etc) is stored in AWS S3 instead of webtask; S3 being an external storage it could in theory be shared.
However, the above just focus on what could be theoretically possible in terms of sharing the most important data and you would still be left with a lot of work in adapting a paired down version of the extension.
Given the extension supports an API (https://auth0.com/docs/api/authorization-extension), would it not be simpler to make your own app that calls into the API?
In addition to that, we are working on having authorization related functionality built-in in the product instead of available as an extension so you may want to check the documentation already available (https://auth0.com/docs/authorization) in order to better gauge how worthwhile would be this specific endeavour around the extension.