The battle of Metropolis was 2 years prior. Superman had won the public favor by the time BvS comes around. It was the US government that wasn't quite sold on him. Lex set up the Africa situation and hired an actress to blame the deaths on Superman. Lex had the man in prison "branded" with the Bat symbol killed. Then he sent the photos of it to Clark. Lex was responsible for the Senate bombing. Lex sent the paychecks with those messages to Bruce. How are none of those significant? All of those played a huge part in getting Batman and Superman to fight.
All Zemo did was frame Bucky for a bombing and then showed Stark a video. All the conflict before that started with the Sokovia Accords which came about after the mishap with Scarlet Witch. Zemo framing Bucky only added a push to an existing problem.
Batman didn't bother with Superman until Lex started manipulating him.
They didn't play a part at all. Not when you realize that Superman never actively escalated the conflict after all of Luthor's attempts. Even when he meets face to face with Batman, all he does is trash his Batmobile and tell him to stop what he's doing. This makes all of Lex's planning and detail unnecessary and redundant. In fact, the
only reason Superman even fights is because Lex kidnapped his mom, why not even do that in the first place if the point was to fight? All of the manipulation nonsense seem like distractions and complicated chicanery.
Zemo's plan relied on things going smoothly (someone here said it's like the Joker's plans in TDK, which I think is an apt comparison), but it was simple and to the point. He added gasoline to the fire by having two factions divided on how Bucky should be apprehended, which is taken a whole other level when Stark finds out about the video. It was effective and understandable, which I can't say the same for Luthor.
Zemo seems to be kinda lucky as fuck whilst Lex kinda convoluted was spinning plates and playing 3D chess. How did Zemo know Scarlet Witch would be incapable of containing the blast? why did the Avengers keep the vision behind? How did Zemo know Stark and Cap would disagree? Any of these parts fell through the whole plan goes to shit
Two of your questions are irrelevant:
- Scarlett Witch's mishap was never manipulated by Zemo, it was a mission that went wrong by the New Avengers during the start of the movie.
- Vision being kept behind had nothing to do with Zemo. Stark had her held so that she wouldn't make the same mistake and as such further damage the Avengers' reputation from a PR standpoint.
Zemo knowing Stark and Cap would disagree is fairly obvious. The Sokovian Accords went into place prior to Zemo making an impact. More importantly, he was manipulating the fact that Rogers wouldn't be impartial about his friend, while Tony would simply do the Sokovian Accords' work in apprehending Bucky, even if he was completely innocent. Furthermore, using the video was manipulating Tony in the sense that he would seek revenge against his parents' killer.