नेत्र = of () + त्र = संप्रदान of न + त्र
Hence, नेत्र means connection to a pull-place
leading = connection to pull place
eye = connection to pull (attraction?) place
root of tree = connect to pull place
woven silk = referring to process of extracting silk
cart = connect to pull place
churning string = connect to pull place
enema pipe = connection to pull place
tubular vessel = connect to pull place = another word पात्र - untill rope place
river = a place to receive pull (from)
Lakshmi = connect to pull (metaphoric) place

https://kosha.sanskrit.today/word/sa/netra?q=%E0%A4%A8%E0%A5%87%E0%A4%A4%E0%A5%8D%E0%A4%B0&scope=kosha