No, we don't. The humans claim that they do, but they may as well be philosophical zombies who claim to have such experiences without actually experiencing them (just as animals don't actually experience pain even if they behave as if they do).
The modern debate about whether LLMs are conscious are not has lots of people whose position is "no, they're not" but with arguments not that much better than Descartes (and also coming from the position of tradition). That's why I bring him up.
> Especially since there is a mountain of evidence proving he was wrong.
Only if you accept a particular way to interpret it. After all, I can show you an experimental proof that apparently the rays of cold (in addition to the rays of heat) exist; but that experiment can easily be re-explained in terms of infrared radiation only.