Engie belgium seem to be using Auth0 as a identity provider. You can find more information about the authentication flow in their documentation. Based on your screenshots, it seems that they use a “Authorization Code Flow”. The doc is here: Authorization Code Flow Documentation
In the meantime, you can see that there is a “refresh-token” in the screenshot. You can use that refresh-token to get a new access-token once this one expires.
I am interested in finding out how to scrape that data and inject it in Home Assistant. If more people are interested, I can work on a python package to do so which could then be transformed into an integration.