The API Management experience in the new Azure Portal is now generally available (no more Preview tag!).
We are also working on transitioning all UI from the Publisher Portal to the Azure Portal. The first iteration of that is the new APIs blade which you may have seen at past presentations. It is now available in public preview to everyone.
The new experience integrates API design and policy definition. For designing APIs there is a full-fidelity form-based UI and also a coding experience built around OpenAPI Specification (it utilizes Swagger Editor). Common policies for modifying the request or response can now be set using a form-based editor as well, while the full XML-based policy editor remains.
Testing APIs no longer requires going to the developer portal and is now integrated into the management surface.
As part of the new design we aim to provide a seamless way to connect your API to other Azure resources as a backend. We are starting with the ability to add a Logic App as a new API or set it as the backend endpoint for an API and plan to gradually add support for other resource types.