I agree that the way today we use gnosticism and the detailed secret knowledge the gnostics had are not the same.
The connection in simplistic terms is the belief that the body is innately evil and can never be regarded as holy or pure, but the spirit of a believer can be, and responsibility for behaviour of the body can be disowned by the spirit until its death of the body happens. This duality is linked by many commentators as a gnostic world view, and certainly I have met enough who 100% believe this, or even preach it on TBN.
One prophet said by just praying give me a new spirit to God, you became an eternal being, and were eternally saved, which they did on a TV show. It was for me very odd, because this had no correspondence with scripture or repentance and faith in the cross and dedication to walk the path of righteousness and reject evil, which is the hall mark of Christian belief from its beginning.
For this reason I call such believers gnostic, but one could invent a new term to describe it, as in it seems these ideas are a new creation. Some have suggested Augustine started it with original sin, and the calvanists amplified it in the reformation. Ofcourse to suggest this is a total new formulation would be difficult for such believers as it would disown what went before, though some would be happy to do this. God bless you
The world of Gnosticism, even in the days of the Bible was diverse. Several "gnostic" sects ran concurrently. Yet one thing in common with them was that they viewed the physical world as defective, and the special knowledge that the "select" would have revealed to them is that we are actually spirit. Matter is evil/ the spirit is pure.
You are correct that the Gnostic influence came into Christian acceptance with Augustine. How much his Manicheanism affected his doctrine of Original Sin, I don't know.