Got it connected. Thanks for the help. I connected to the TEG AP and ran the wizard to set it up with my WiFi credentials (instead of the cellular connection it was set up with originally), then restarted it and it started transmitting through my network. Set a permanent URL and now Hassio happily reads the sensors as you listed them at the top of this post.
I was about to try building a component and found that I can’t do that with Hass.io, so I’ll change over to Hasspian. Tinkering is more my thing so Hassio wasn’t really for me anyway, but I’ve a lot to work through before I get there. The custom sensors you wrote above are presumably used when customising Hasspian? Hass.io has just listed the sensor data on my homepage and I can presumably run automations off that. My plan is to turn on the heating if it is mildly cold in the morning, if I have battery left (and turn it on regardless if it is really cold). I can probably do that in either system but I have a few weeks to learn Hasspian before my AC is installed anyway.
Thanks for the help.