This module behaves as a switch. All you do is turn on the switch in software.
A relay also behaves as a switch.
All you’re doing here is trying to build a series of switches… each switch however is able to switch more and more current and at different voltages, so it’s possible to use milliamps at 3v3 to switch amps at 24v with your relay.
Your software switches a port on, and a relay then activates, and then your load that you have connected to the relay turns on. You turn it off in software, load-module turns off, relay turns off, load turns off.
Your relay will have two sets of contacts. You need to understand what those contacts are and make sure you’re connecting to the correct ones. Show us the relay you’re using if you need help pointing that out.
To start to figure this out, step away from a microcontroller. With your load and your relay, make sure you have that working so that when you energise the relay your load switches on (I suspect your 6.4v measurement is telling you that you have the wiring of the relay not worked out properly). Then, once you know the correct pins there, connect the relay and load-module as shown in the example pointed out earlier and everything should work as expected.