Well, you described it quite clearly in a few sentences here, I definitely would not think this is something that cannot or should not be addressed in conversation. Perhaps also likely you are projecting things into that part of your therapy sessions.

I had two T's who were both friendly and welcoming when first seeing and greeting me, but not overly. They differed a lot in how they started their part of the sessions though. The psychoanalyst I saw first would just leave his door open when he was ready to start (or come out to get me in the waiting room), always stand up and say a friendly 'hi' when I entered and waited for me to sit down before he did. Then waited for me to start the conversation, he would not say anything first but I never stayed in silence. Never asked how I was or anything else. Second T always came out to get me and the conversation started just as naturally and in diverse ways as it typically does in ordinary meetings. He often asked how I was doing, or we engaged in a bit if small talk for a minute, or jumped straight into the deeper waters. He was friendly and welcoming in a way that felt natural for me, not contrived and never condescending. Not sweet and sugar coated (that I would dislike), just friendly and treated me as an equal, not as an authority. I did sense subtle mood differences in how he greeted me but did not discuss that more than once, I simply thought everyone has those subtle fluctuations and he did a great job trying to stay even.

I interviewed T's whose greeting style felt aversive for a variety of reasons. It can be a good discussion topic but also I just felt I worked better with someone who naturally matched my style and preference for interaction. I also met Ts who appeared very intrusive, that was even worse. I know why I dislike intrusion already so I would not see one of them just to explore more.

I personally like better when people look at me with a friendly expression rather than indifferent but from Ts I prefer if it's a professional kind if friendliness and they do not pretend to be my friend or a relative.