This is kinda funny, and I know the concept of “authentic” isn’t particularly easy to nail down, but my experience is that Italian lasagna doesn’t have tomato sauce. It’s always been thin pasta, a ragu, and bechamel. It generally changes to match the tastes and ingredients of where it’s being made, but maybe you’d like the version I know.
I had moussaka in Greece a few years ago and liked it too!
As someone who makes pizza from scratch every week, I love all forms of pizza from fast food US pizza (like Dominos), to “drunk” US pizza dipped in ranch, to NY pizza, to Chicago deep dish, but what I make at home is always simple Italian pizza with just a few ingredients: dough, a sauce made from San Marzano tomatoes specifically canned for pizza with some salt, fresh oregano, mozzarella cheese, and olive oil. Sometimes I add a ton of arugula on top too. What’s nice is that pizza is also kinda healthy actually.
It’s very common in the US to just plop some pasta sauce on top of noodles for one thing… You gotta cook the pasta in the sauce real quick! If any American reads this and doesn’t do that I promise that tiny change will already improve your pasta experience.
Ragu is a general term for meat sauces some of which have tomatoes but not all. The recipe I use I wouldn’t call a “tomato sauce” but it has tomatoes. In the US most ragus are much more tomato forward if that’s your frame of reference.