From what I understand, the issue with lab-grown diamonds is that they can't really grow them beyond a certain size at this time. I think clear ones are a couple of carats, and colored ones are roughly double that. I could be off a bit. Regardless, that's not huge, though I don't know what size they require. Maybe it's sufficient.

So they can probe/measure the contents with light, usually in laser form.

Contents are completely enclosed by diamond to hold the pressure. No way to probe otherwise as far as i know.

People interested in high-pressure chemistry follow what's happening with spectroscopy, UV/Vis or infrared. Fig. 3 on p. 376 has the Raman spectrum.