How to migrate Energy and Recorder data to new system?

I migrated my configuration (full backup actually) to a new system, since I wanted to use HA OS instead of the (unsupported) supervised installation.
That went fine, but all historical data seems lost (apart from the InfluxDB data that is correctly transferred). The Energy statistics are empty, and all sensor data from the past days is gone too. How can I migrate that? A full backup and restore apparently does not include that correctly. And I wonder if it should. But anyway, I’d rather have it restored, especially the Energy related data, PV production, gas consumption, over the last year. Do I do something wrong, or should I copy certain files explicitly that are not in the standard backup?

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