I don't know what your view of total depravity is, but to the degree that some reformed doctrine takes it - i.e., that total inability exists even after regeneration - it it is definitely gnostic in character.
It is Biblical. I posted the verses about it. Any similarity between gnostic beliefs is possibly due to those recreating the gnostic beliefs. There are no writings from the gnostic believers. We only know their beliefs from Christians and others arguing against them. Thus they are then somewhat flawed.
At my stage in life I am only concerned about what the Bible says. When I was an elder and deacon in the 3 churches I served in (moved 2 times) I was concerned about understanding the different heresies. But now at 73 without those responsibilities my only concern is what the Bible states.
For your information I find Google is a good tool to find location of Biblical concepts. What I quoted came from Google pointing me to the text then going to biblegateway.com to select chapter and translation. Then cut and paste the selected text onto the site.