I've experienced that throughout my life, for many years it was pervasive. Part of it was my situation in life, where I felt like I wasn't able to be honest about who I was... yet even after that was resolved I still do experience that feeling to some degree. For me, it is this sense that we are ultimately alone in terms of being responsible for our own lives; I cannot make someone else's choices for them, they cannot make choices for me.
And there is always a gap between the total reality of who someone is vs their ability or willingness to disclose that; we will never ever know someone else 100%, and truly we don't even know ourselves 100% either. Even when we coexist in the same space, we are still seeing the world a bit differently, each of us having our own past and our own psychological and biological makeup, so we will never 100% share a world with another; we all live in separate worlds so to speak. It's a rift that cannot be crossed.
I think some people are very aware of existential distance, others don't really seem to notice it. Those who are more literal-minded tend to feel lonely when others aren't around and feel happy when they are engaging others who are around; the more existential-minded can tend to feel loneliness even when someone is there and engaging. It lingers.
I did note that self-acceptance helps lessen it. When you are not able to be honest about who and what you are and end up relating to others through a mask, that only exacerbates the loneliness. (Because the person that people know and are relating to is not you, it's just a facade; therefore you really are alone.) I've found that the few really close friendships I've developed where people know "me," they are fierce connections and I feel a lot of joy and relif within those relationships. On some level, I sense we are still alone ultimately, but it doesn't bother me nearly as much; I accept that they love me for me, and would love me even if they could find out everything about me, so it's like the willingness to accept and love is perceived as connection and closeness even if the gap of Knowing can never be crossed completely. Rationally, maybe we're still existentially alone; but I don't feel painfully alone when I'm with them.