As of today, this API worked for this kind of request with a private access token in basic auth (no username, only PAT in password) in Postman:
https://ORG.extmgmt.visualstudio.com/\_apis/ExtensionManagement/InstalledExtensions/ms-devlabs/team-calendar/ExtensionDataCollectionQuery
Body: {"collections":[{"collectionName":"TEAM_ID.7.2025","scopeType":"Default","scopeValue":"Current","documents":[]}]}