Using µW in Utility meter or statistics

Following the resolution of my previous problem described here, it turned out the my EV charger is supplying energy consumption data in µW and hence I can’t set it up directly with utility meter or statistics card.

I was trying to create a template / binary sensor and although it’s converting the units fine, the new entity is not recognised by statistics nor by the utility meter .

Data is supplied via modbus / sensor , code below. I’ve added unit_of_measurement: Wh for it to be recognised by statistics card but it’s obviously wrong.

Any ideas on how to display the data in HA recognisable unit would be appreciated. Thanks!

- name: "Wallbox - Real Energy Consumed Phase Sum"
        unique_id: wallbox_real_energy_consumed_phase_sum
        scan_interval: 10
        address: 1692
        count: 2
        data_type: uint32
        device_class: energy
        state_class: total_increasing
        unit_of_measurement: Wh