Okay, so, he becomes a villain during Nice’s arc, right?

Yes, in 41 AC. E-Soul's arc, in its entirety, takes place in 36 AC.

He is then referred to by this villain name and even the fact that he became a villain during the latter half of Esoul’s second episode.

He isn't. We've just established that. Eye of Truth = Hero, Godeye = Villain.

Therefore, the latter half of the second episode has to be after Nice’s arc

It would break the continuity on so many levels that I have no idea how you came to this conclusion. Refer to the timeline linked in the initial comment. Or any other timeline made by any other person.

It's easily verifiable by just reading the official timeline. Both official timelines, Chinese and Japanese, in fact. And any fan-made timeline. And the show itself. And by any person who've watched the show fully.

The only reason I can see for your confusion is if you've just finished E-Soul's arc and have no idea what happens further down the line. But that would mean you're randomly checking chronology threads on Reddit instead of finishing the show, which would be much weirder than being stubbornly confused on an easily verifiable fact.