Entschuldigen Sie die dumme Frage, aber ist der sanfte Schlag ins Gesicht eine übliche Begrüßungsform unter männlichen Freunden in Italien? Ich kenne das nur vom Fußball und Tennis und jedes Mal, wenn Matteo gegen einen Italiener spielt, begrüßt er ihn beim Händedruck so.

It’s more of a respect gesture from an older player to a younger player. Something like “now that you’re grown up you can stand this slap”

Commonly If you do not have a very high level of confidence with the person you slap, it could be used to disrespect him by comparing him to a child:
This gesture is commonly used with chidrens, to compliment them in case theyy are acting good or when they have done something special.

In some regions of southern italy like Apulia, this gesture could be used to act as a friend.

It is a gesture that claims fatherhood. It could be used also when a more experienced person greets a young one. Like in this case.
It is a gesture of protection: “finally you arrived here”

I would say it’s quite common in Italy, in my mind it’s usually from someone who is higher in whatever hierarchy, or an old guy to a young one. Here however I found it a bit disrespectful from Berrettini, even though he is older than Sinner but he’s also lower in the rankings. I think it was something like “ok kid you the best one” in this case, but perhaps was a bit too much.

It’s a greeting an older person would do with a younger one.
It’d not look as smooth if the younger counterpart were to do that.