Please don’t resurrect old threads!
As you imply: there is no provision for battery levels in the official RESTful API used by evohome, but there are error messages in the device state attributes for (inter alia) flat batteries.
For actual battery levels (and other features), you’ll need to use something like this:
https://community.home-assistant.io/t/honeywell-evohome-via-rf-hgi80-hgs80