Every now and then I come upon claims about the "unique randomness" of digits in the PI number; about how it is all mysterious and deeply chaotic, and about how potentially any given finite sequence of digits can be found in it if you look long enough... Here's an example from a educational math-related video.

But would not the same be valid for most irrational numbers, like sqrt(2) or sqrt(5) for example?

I can see how we can not exclude the possibility of digital sequence of PI being potentially different from that of other "common" irrational numbers, in some way or another. I can see how, say, digits in the PI number could potentially follow some slightly different statistics than those in sqrt(2). But are any of these claims actually proven? Is there any reason to say that PI, but not sqrt(2) is "uniquely random", "non-repeating", "mystical", perplexing etc.?

Thank you!