I first experienced this "falling away into connection" 40 years ago using LSD, but over the last decade I've arrived there without drugs.
Along the way I've explored a lot of non-dualism, including Buddhism, Taoism, Advaita (which is the purest form I found) and various flavors of monistic idealism. There is no "I", but it turns out that there is also nothing else real either. That makes the question of what "I" might be connected to, or what that "oneness" actually is, a wee bit problematic.
The process of deconstructing and seeing through one's entire belief system is similar or identical to what a lot of modern non-dualist teachers describe as the path towards enlightenment. I don't use that word, it makes people think funny things.
My original goal was to find out the deep truth about what was really going on in the world, and why. What I discovered was so existentially disturbing (as in, everything I believed turned out on closer examination to be a lie) that I changed my goal to that of somehow finding ongoing peace of mind no matter what the circumstances (i.e. to end my own suffering.)
The only way I could find the complete peace of mind I was looking for was through radical acceptance - acceptance that any belief I examined closely turned out to be erroneous, so by inference there is no reason to hold any belief. So I've worked on discarding them all, as my OP suggests.
So far, so good.
PS: When I began this whole process I was a very strict scientific materialist, a position I'd held for 55 years. This was one of the first belief systems I questioned when I began my search. I still operate by it when I have to, because the world appears to be a physical place.
I now think of my worldview as a superposition, in which dualistic materialism and monistic idealism each operate at different times under different conditions. This is much like quantum superposition which allows an electron to behave as a wave or a particle depending on the conditions.