How much information does a widget config MFE have access to

Can the config MFE get the current user or use the api-manager to make API calls using the infrastructure in the app-builder?

Potentially it could, it’s up to the developer. We don’t provide out-of-the-box frontend libraries to do that but the dev is free to make API calls as needed.
The only constraint we have is: MFE should have a config property where AppBuilder can read/write the widget configuration.