Is it possible to discover types (e.g. via GET /)?

Assume a generic client is just pointed to any JSON:API endpoint, i.e. is not familiar with the types and fields. Once you find a “starting point” like /articles, you can get resources, discover fields and related types and resources.

Is it possible to get a list of types? I’ve seen some discussions on adding this in the meta descriptions, but it does not seem to be a required part of the spec.

This is not covered by the JSON:API specification itself. It could be standardized using an extension.