How to gain intuition around the hardware & software relationship?

What are your goals, exactly? There are multiple ways to answer this depending on what you’re trying to achieve. But for someone who maybe just wants to program hardware, I think learning embedded systems would be interesting. You can also just get an FPGA to experiment with programming it to do different things. Additionally, there’s a whole world of hobbies related to Arduino, RaspberryPi etc. microcontrollers. So basically, embedded systems. Good luck.