As an italian who is told he's pretty good at cooking, some of this is on point but a few things sound "wrong" to me (I use quotes because there's really no objective way to do this literally right or wrong, I'm just comparing with my experience / what I perceive "we learn from grandmas"):

- Put the pasta into the pan with the sauce (which I guess is the main point of the article which starts off with "italian" restaurants putting sauce on top of the pasta in the plate): defintely yes, but...

- Add pasta water: it depends on which sauce you prepared and how you prepared it (and the type of pasta... not just shape, but fresh -vs- dry, and what it's made of). When one uses "pasta water", it's usually in the making of the sauce, not before putting the pasta in the sauce pan; sometimes cooking water is added to the sauce if it "shrinked" too much or the ingredients are not of amongst those which attach to the pasta well, but these are their own cases. All that "adding water and stirring" to get to the "perfect texture" might appear to make sense, but I'm pretty sure it will take too much time and it will mess your pasta consistency because it will get overcooked. Sure you can under-cook the pasta alone a bit to compensate, but what's the point in that? What I'm trying to say is that this trial and error thing might make sense for someone who does it for the first time, but after a while you figure out how the sauce ought to be in the first place, you put the past in, jump it (as in, move the pan to make the pasta "jump" in it so it doesn't attach to the pan) to the right consistency and everything gets where it needs to be pretty easy without all that fuss. At least this is what I do and what I see others that seem to really know how to cook (based on the results) do.

- The bit about using cooking water (that's another way we call the "pasta water") to adjust the consistency which turned bad because of the cheese thickening and liquids evaporating... well, unless we are talking about sauces which have significant cheese quantities in it (e.g., the "cheese and pepper", or "4 cheeses pasta") and have a different process on their own (as does the mentioned "carbonara", which I guarantee you'll screw up if you follow this process because you'll cook the egg too much), cheese usually goes on top of the pasta in the plate as a garnish. For some sauces (e.g., the "amatriciana"), you're even supposed to make the plates (with pasta already mixed with sauce) get a bit less hot before putting in the cheese, to avoid it melting too much. Putting cheese in the pan for a non-cheese based sauce and make it melt and then thick is sort of a cardinal sin (you can add all the "pasta water" you want, you'll never get it back to where you need it to be and it will mess up your dish)

- Add fat: what? Just, no. Olive oil is of very common use, but you don't add it "to the sauce" for texture, for most sauces you use it as the base for the sauce. Butter? Unless we are talking about a butter-based sauce (e.g., butter & sage), which are not that many or very common anyway in regions but the northern ones, nope. Not like that. Some add olive oil as a garnish, but again really depends on which sauce you are using, and it ain't that common