However, when I manually create another backup with the latest version (2.099), the format looks like this:
Independent from the format, the API description is not clear on what it expects as parameters in this situation. I would expect to POST to an endpoint like volumio.local/api/v1/restore/my-web-radio with the backup file as request body.
In this file: MyVolumio/docroot/modules/myvolumio/src/Api/myvolumioApi.php you can see where I’m saving a list of radio stations by accessing the “backup” component of the Json object I got back from Volumio’s API call: