Reading through these excellent explanations, the simple and the more complicated, highlights something for me. Boyle's law (which is at the heart of the OP's question) is indeed covered in PADI OW (and I imagine in the equivalent in other agencies as well). But in the case of the PADI course at least, it is done at a level that a 10-year-old can understand. It's very basic. And for me it wasn't until I got into the water (and particularly only over my last 20 dives or so) that I started to understand what it really
meant in practical terms.
My buoyancy control has improved tremendously since my initial dives. Especially at depth - I rarely touch my BCD throughout the dive; not much need for it. I attribute part of that to a dive computer that is
extremely sensitive to ascent rates - I have a nickname for it due to its sensitivity (and wear it on my right wrist so that it doesn't start complaining just because I lifted my left arm to adjust the amount of gas in the BCD). So I've learned (with the help of "Screamin' Leo"

) how to ascend slowly during the deeper stages of my dives. I have gotten to the point where I rarely have an "ascent alarm" during the dive - until I get to the safety stop.
With the exception of exactly
one dive in my log, I
always have an ascent alarm at the end of the dive, because I still need a lot of practice to properly control my ascent rate in those last 5 metres. Boyle's law is the reason - and of course the last 5 metres is the absolute
worst time to be ascending quickly (again, because of Boyle's law), so it is my top priority in "skill development" at the moment.
So much of scuba training is "theory". It isn't until we get into the water that newer divers like us start to understand what it really "means".