Thanks Kris, that helps!
Meanwhile, I have indeed gone down the path of using my audio card in-line and while the first attempt did not produce any results, I realised I had not paired a plug yet, so I paired a plug and then the RC started emitting the expected codes - I guess that made sense to anyone with some experience in the field lol.
I used Audacity and bought a cheap ear-set for $5, ripped off one earpiece and used that to connect to the RF receiver's data pin.
I wonder if the Arduino will also start recording the codes now, I will post a follow-up to confirm.
I am not sure if I will continue down this path because the box of plugs says the codes are changing, so it may prove hard to hack that RC for my project if I need to figure out the algorithm... The other thing about the RC of my plug is that it does not have any soldering, so I am not sure if I can reliably just integrate the PCB board on my own circuit to bypass the decoding requirement altogether because it is not obvious where I need to solder the wires to.
Cheers,
Gaetano.