The Shaykh’s clarification that greeting every person in the gathering individually when shaking their hands is an additional innovation.

The Shaykh : And recently, I pointed out something I understand from the Sunnah, which is: the habit of some people when they enter a gathering, and there are some individuals in the gathering with whom it is customary to shake hands—shaking hands is undoubtedly prescribed, but before that comes the greeting—some people today, in this era, and it was not the case before, when they enter a gathering and there are, for example, five people, say: “As-salamu alaykum,” “As-salamu alaykum,” “As-salamu alaykum,” giving the greeting five times, a specific greeting to each individual when he shakes his hand. This form is also an additional innovation, because we do not find in the Sunnah, when we hear Abu Dharr (may Allah be pleased with him) say—as I recall it was Abu Dharr— This is undoubtedly one of the newly invented matters. The one who enters should offer his greeting to those present, a single greeting, unlike the greeting for seeking permission when knocking on a door, where the Sunnah is to greet three times, because there is another purpose there, which is to alert whoever is inside the house to the one knocking. Our discussion is about gatherings that contain a number of people, so it is not befitting to give each person a specific greeting. Rather, he enters and addresses everyone by saying “As-salamu alaykum.” Then, if he sees that it is easy for him to shake hands without difficulty or without feeling awkward, he does so; otherwise, he greets and sits wherever the gathering leads him. Yes.