(It disputes the details of the traditional 'to the city' etymology, but in the end proposes deriving from something else with very similar meaning, "στην Πόλι" (something maybe like 'sten Poli' but there are details of historical pronunciation in the article I didn't read closely) rather than "εἰς τὴν Πόλιν" [is timˈbolin].)
Without reading the article, if it is between "στην Πόλι" and "εἰς τὴν Πόλιν", I can tell you, as a Greek, it is exactly the same phrase. Poli/Polin (Πόλη/Πόλιν) are interchangeable, the same word with a different suffix but with both the same purpose, and "στην" is just "εις την" stiched together.
"THE ETYMOLOGY OF İSTANBUL: MAKING OPTIMAL USE OF THE EVIDENCE"
https://ruj.uj.edu.pl/xmlui/bitstream/handle/item/15924/stac...
(It disputes the details of the traditional 'to the city' etymology, but in the end proposes deriving from something else with very similar meaning, "στην Πόλι" (something maybe like 'sten Poli' but there are details of historical pronunciation in the article I didn't read closely) rather than "εἰς τὴν Πόλιν" [is timˈbolin].)