I would like to add my (unsupported) solar panel data into ‘Home Energy Management’ in HASSIO but unfortuantly the only way solar is supported is using a ‘clamp’ or a energy device which is supported as ‘energy integrations’.
My solar panel data (brand is Afore) comes from a JSON call using ‘platform: rest’. The entitites I get this way are not available in the selection ‘Home Energy - Solar’.
How can I make them available / use them to provide my solar data to Home Assistant Energy?
If your inverter offers something of an API, we could build an integration for it so that you simply have the data available as entities directly 
You don’t need a full integration. The entities just need to be configured with an appropriate device class and a state class in order to be selectable for energy monitoring. See Sensor Entity | Home Assistant Developer Docs for the various options.
Here is how I monitor my solar although it is using esphome custom integration so would be different but you can see the device and state classes I have set in the yaml: xantrex/xantrex.yaml at 88621569f94ebce58764f2874951d4034b49e308 · clockbrain/xantrex · GitHub