@thecrawford Wyse 5070's are great for exactly this! I've bought a few from this listing (US listing, $39): https://www.ebay.com/itm/356344851574. Right now they are out of stock, but they usually come back in stock in a few weeks. J5005, 8GB RAM, 64GB SSD, very reliable, low power.
Some of the Wyse 5070's have a slower CPU, less RAM, or eMMC instead of a proper SSD. Probably still fine for HomeAssistant