How does hydrostatic pressure of the ocean affect air density in a closed system, like the lungs, or a scuba tank?

I’ve never understood this. The deeper you go, the more compressed air is, the more air you need to fill your lungs.

This would make sense if your lungs were like… outside your body. But they aren’t. They’re inside your body. One explanation I’ve heard is that the actual air canister becomes increasingly compressed/pressurized, the further down you go. But this doesn’t make sense - there is no interface through which this pressure is transmitted. The canister doesn’t shrink. It’s a pressure vessel - that’s the whole point.

Gas concentration in the blood also confuses me, with regards to this. I understand that ascending from depth too soon can cause dissolved gases to precipitate out (sublime? Idk)… this has something to do with the pressure - high pressure means higher solubility. A drop in pressure means lower solubility. But your circulatory system is closed (atleast, when imagined simply) - so what is the interface between the ocean’s high pressure and your blood? How did excess gas get pushed into your blood, if you didn’t like… try to breathe the water, and actually give all that pressure an interface to your circulatory system.

And if the pressure difference in your blood is high enough to dissolve crazy amounts of gas, how is it not also high enough to just kill you from high blood pressure?

It would make a lot more sense if being underwater squished you down to half your size, like a balloon under water. I’m pretty sure this doesn’t happen though?