Caves are openings in rocks that were (often, there’s also caves in result of tectonic shifts) dug by water or lava and hot gasses. They already applied a lot of pressure, and rocks that could withstand that pressure, are what’s left. Other rocks were dug out.
Underwater caves can have high water pressure – it’s about compressing gasses and liquid, not rocks. Air is much easier to compress, so caves filled with air, even deep ones, do not have high pressure. Because if you compress air, it’ll just escape into areas of lower-pressure air. Water cannot be compressed whatsoever, so it’s just holding all the weight. Also, air (our atmosphere) **is** what is keeping ocean surface intact and pressures in the bottom high. If we had no atmosphere, oceans would also just boil away.
Think of a piano falling on you, and a sofa. Sofa compresses much better than a piano, so it’s likely to do less damage than a piano (you’ll experience much less pressure).
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