I'm able to successfully fetch information regarding the latest version of an app from the iTunes Search API, and information regarding Test Flight versions from App Store Connect.
However, I would also like to be able to get information about any phased releases currently in progress. Is this possible using either of the APIs?
Using App Store Connect:
First, get the version list for your app, using the URL below. The first version in the list will be the newest.
https://api.appstoreconnect.apple.com/v1/apps/{YOUR_APP_ID}/appStoreVersions
For each version, fetch the resource at the URL in the relationships property:
version.relationships.appStoreVersionPhasedRelease.links.related
The value in data.attributes.phasedReleaseState will be ACTIVE if the version is currently in a phased release state.
There might be a more direct way of fetching all phased releases directly, but this is how I solved it.