Wowza! $20 per relay (+shipping) is a lot! And I thought $6 each was a lot.
I think the second one would work with 3V, but I question DigiKey’s claim that it can be activated with 1.2V when the datasheet says the typical input voltage drop is 1.42V and a max of 1.56V. So a word of caution there since none of those numbers seem to match.
If we assume that we either have 24V AC or 5V DC coming in (many of us are not fortunate to have a common line in our HVAC system), we can assume there could be a 5V DC rail and a 3.3V rail. If we have those, we should be able to use transistors to trigger the relay much like @HestiaPi did in the clicky edition of the ONE. Details on that are here: PCBA Info – HestiaPi
As a hardware supplier, I’d be pretty interested in being able to use one of the existing models of relays (solid state or clicky) that I already have in stock. Ideally, designing to support both of them for silent or noisy operation. Having said that, I understand if the new design requires new components.