The goal is to 24V control signal YEL (cooling) and GRN (fan) for a Florida storage building, with three AC units. A single board computer (Raspberry Pi) is outfitted with 2.5 Ampere relays.
Is there any reason to believe that higher Amperage relays are needed?
Perhaps the better question is: What is the maximum current for thermostat wiring?
I think the answer that you want is that the 24v is only used to close relays, so the amperage needed is only for the combined amperage of the coils on the relays (or not combined if you're using one relay on the board for each control wire).
I would assume that a 2.5A relay is more than enough for each control wire, but if you are trying to drive all three units from one relay, you might start to run into issues. For instance, if the coil you are driving takes 1/2 an amp, you're ok, but if it takes 1A, and you need to drive three of them, the Pi might start to have issues. If you are going to combine green and yellow you are powering 6 coils, then you're probably going to be over amperage - it just depends how you plan on wiring and controlling.
The relays on the control boards of the HVAC might be marked with the coil voltage and amperage, but you might just have to measure it yourself. Even if the amperage is too high (or just to be safe), you could use the Pi to drive a higher amp relay that in turn will switch the control wires.
To start off with, with any low voltage DC product like this, the product is only as good as the components. Fortunately you linked the Amazon page, and it has some HUGE photos, so we can identify the relay in question: Songle SRD-05VDC-SL-C. Let's go pull the data sheet, eh? What do we see?
Not a well-known and reputable brand of relays. All Kanji, without any simpler Hiranaga nor Katakana, means Chinese not Japanese. Uh oh.
Alright, well, if that's really true. cЯUus = the UL/cUL mark, and the funny triangle is TUV. Both NRTLs, note the ЯU mark is a component mark not a mains-rated equipment mark, but then, this is a component, after all.
Well, that's good; that makes it a mechanical relay, which means we're guaranteed no weird GND-loop problems that you might have with silicon "relays".
You're not switching resistors here; you're switching big fat contactors with coils. Coils have inductive kick, which will cheerfully arc across the contacts if you don't stop it. That's why you need to use the inductive rating. Now is 3 amps enough? Let's look.
The common furnace transformer is 40 VA @ 24V. That means its capacity is 1.6 amps. Realistically a contactor has to be reasonably under 0.5 amps for multiple ones to be able to be on at the same time. So it looks like a 3 amp inductive relay ought to be able to handle 0.5 amps. If you get burnout/welding/sticking of contacts, you may need to come up with a snubber to dissipate that inductive kick, noting it'll be an AC snubber.
Thermostats take R, and connect it to either G, W, Y, or other wires as called for by system design. As such, R goes to every relay, and G, W, Y, etc. go to a relay of their own.
Having 2 transformers in the system usually means they meet somewhere, with one wire of transformer 1 tying to one wire of transformer 2. It's perfectly possible for that connection to be out of phase, meaning the other lugs of the transformer are now 48 VAC apart. That can fry stuff if you're not careful.
