Why not set up backups for the Proxmox VM and be done with it?

Also makes it easy to add offsite backups via the Proxmox Backup Server in the future.

Additional information regarding Home Assistant:

The sun component (which should be enabled by default) already computes the sun position for you.

Elevation and azimuth are available as standalone sensors sensor.sun_solar_azimuth (might be disabled by default) or as attributes on the sun.sun entity.

Not an expert but these systems are fairly self-contained and robust. A few things that can be checked easily is that the fan spins, the radiator is free of debris and some compressors might have a sight glass for the oil level.

Any other checks regarding performance of the system, leaks and refrigerant level require you to perform a full refrigerant discharge and recharge. That takes special equipment and some time so no one in their right mind would do that for free, unless they can then force/guide you into some kind of upsell situation.

Larger systems might have some kind of oil filter/catch-can that you might be able to check easily but I’m not too sure on that.

After all heat pumps are just plain old A/C units with a reversible cycle.

I don’t have any experience with it but this might do something along those lines(?):

https://esphome.io/components/binary_sensor/ble_presence.html

Seems like you can just add it to one or more of your existing esphome devices.

If you have such a system up and running already you could try to modify it before ripping it out and starting from scratch.

Borrowing an idea from the machine learning approach you could additionally take the difference in average outside temperature yesterday and the average forecasted outside temperature today. Then multiply that by a weight (the machine learning approach would find this value for you but a single weight can also be found by hand) and subtract it from the target temperature before the division step discussed previously. Effectively saying “you don’t need to heat as much today since it will be a little warmer”.

I fear that’s about all you can do with this approach without massively overcomplicating things.

This is effectively what a thermostat does.

The problem is that the controller won’t know how well insulated each room is, how cold it is outside (including wind speed), which doors and windows are open and when, what people or devices are doing in each room.

The way thermostats solve this is by creating a closed loop where they react to how the room reacts to their actions.

Depending on how your heaters work you’ll likely need some dynamic component to react to these unforeseen changes unless you can live with the temperature being very unstable.

To get a rough idea of how long the heaters will have to run you can look at each room in for the last n days and see if the heater’s runtime was long enough to (on average) hold your target temperature. Dividing the average temperature with the target temperature will give you an idea whether they were on for too long or too short. (If the heaters have thermostats you’ll likely need to subtract a small amount from that value so that it will settle at the minimum required heating time)

If that value is close to 1.0 you know that on those days the heating time was just about perfect.

Once that is the case you can take the previous days heating time and divide it up over the cheapest hours. The smaller of a value n you choose the more reactive the system will be but it will also get a little more unstable. Depending on your house and climate this system described here might simply be unsuitable for you because it takes too long to react to changes.

There are many other ways to approach this very interesting problem. You could for example try to create a more accurate model incorporating weather and other data with machine learning. That way it could even do rudimentary forecasting.