I suspect, since it's a one-sentence answer, that the longer version would be more complex. (See below.)
Even with only one Italian grandparent, the Italian traditions stay very strong in my family, and my extended family, which is large and close. We pass down the recipes from my great-grandmother, we all make our own bolognese/marinara sauces, which we learned to cook at the elbow of grandma or grandpa, and every family gathering includes at least one big Italian meal. But, because we're also Americans, it ends with pie.
I'm the only fluent speaker of Italian in my family, now that my grandfather is gone, (he spoke only dialect,) but various others, including the young generation, have studied it, and speak some. One of my nephews will do his study abroad in Italy. My own family took a trip together to visit where our people came from. And let's face it: nobody hates to go to Italy.
All of this to say that, even though we've got a mixed background, certain traditions from the Old Country linger strongly. But you can't decide for other people how much they embrace their new country, and how much holding onto family traditions means conflicted loyalties. Just because Denis Shapovolov and Alex Zverev might embrace or appreciate their own Russian roots, (or not,) who's to say for them that they don't "feel" Canadian and German, respectively? Where you grew up, who your friends are and the cultural coding that you grow up with matters, too. Maria Sharapova has spent essentially her entire life in the US, and yet her choice "feeling" for herself is that she's Russian. Living in the US is for her tennis. For her, it's went the opposite way.
BTW, I meant to say earlier...your English is very good, and completely up to this conversation. I appreciate your candidness.