What voltage are you planning to run through PoE?
My switch will output ~48V as per the 802.3af. I was thinking of using something like this (sorry, not sure if links to merchants are allowed! Please feel free to remove if not!). This will provide power through USB. I’m still confused on how to add Ethernet though 
I’ll open a new thread as soon as I get there!
It just struck me… HestiaPi needs 2 wires for power (L - line and N - neutral) and 2 wires (H - heating and W - Hot water) for outgoing signal to your heating system. All the 4 wires are usually coming from the same single system (furnace?). The voltage that your system is expecting to see is the L that was provided by itself.
If you introduce your own DC power from your switch there will be no power on L and N so nothing to return to the W and H contacts,
Unless you hack the board a lot or your system is seriously different from the rest of the world, I don’t think PoE will work. Additionally (again unless your system is seriously different from the rest of the world) you don’t really save any power cables as these cables should already be in place on the wall waiting for a thermostat to be plugged in.
Apart from that, your link looks OK and you will need a MicroUSB-to-Ethernet adapter (check compatibility with RaspberryPi first) but if you plan on plugging in the MicroUSB you will see that the USB for power is blocked by the relays. The only USB left is for data where your MicroUSB-to-Ethernet adapter should go so you would need to cut the USB plug from that PoE adapter and solder it directly on the +5V pin.
If you are not very confident about that, ask a friend who does or this forum 
Good point. My idea was to provide a stabilized power line to the rpi0: the PoE switch is backed up by an UPS, the furnace is not. However, I didn’t think of the implications for the H/W lines, good call.
Just to clear up my mind: would this prevent using L/N for powering and the USB just for the ethernet adapter? i.e. should I still solder something even if I stick to use the mains power? (Maybe I should just create a new post in the forum :D)
Please do and I will reply there instead of highjacking this poor thread
Admins have magic powers, so I’ve moved these posts to a new thread for you. Welcome @dexterp37 !
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No, it would not prevent. You can still use L/N for power and the left-side USB for the USB-to-Ethernet adapter. Here is a list with working adapters. If you find one that is working for you feel free to post it here, at least the model. Don’t see a reason not to include a link too.
Thanks! 
Now, back to my original plan: the idea was to use PoE to have a stabilized source of power for the HestiaPi and do without a wireless connection. I have a few options:
- Usb power (no soldering), but that creates problem for controlling the furnace (USB can come from POE using a splitter); I won’t be able to use the Usb TO Ethernet adapter in this case.
- PoE → PoE splitter → Power soldered +5v: this would make everything work just fine, as long as I don’t plug the L/N cables in but only the signal cables; I would still be able to use the USB port for the Usb To Ethernet adapter.
- Power from L/N cables + Usb To Ethernet Adapter: this would work for the LAN part, but I would still have an unreliable power source for the HestiaPi.
Does the above make sense? Moreover, does it make sense to go through all these efforts to have a stabilized power source for the HestiaPi? I’m not quite sure how a sudden power loss would influence the system, so I might be overthinking this. Clues?
You can still do that if you modify the PCB. 2 changes are needed. 1 to obtain physical access to the right-hand-side USB which is currently blocked by the relays. Then you would need to still connect the L wire and not the N in order to send the L signal down H or W when each are activated. I have never tried that so please make sure it is safe both for you and the Pi.
The second modification is also needed for your second option labelled “PoE → PoE splitter → Power”
A power failure (if coming from furnace) would reboot HestiaPi so till all is back up it may be a few minutes. Then again, I wouldn’t know how often this can happen in your house/area.
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Thank you very much, everything is much clearer now!