A point about using engines and looking for an advantage in the English Opening: I don't think you play the English to get an opening advantage. It is a strategic opening where everything is basically about cheating the opponent in relation to potential pawn structures etc.
Replying c5 in English opening as white

Not sure if this is what you were looking for but this seems like an interesting way to get imbalances with opportunities for both sides. After looking at this position with stockfish and a book on the English, I realized that white has several moves that look pretty interesting. Stockfish keeps switching what move it likes but I personally like g3 after this because the positions that can arise seem quite interesting.
So, i was analyzing professional matches following that line, and they pretty often lead to an equal position with constant draws:
From this point, most games leads to a draw, and the win rate is balanced for both sides.
And then, by following most played moves by professionals:
The engine points e6 as being best next move
Castling now leads to these lines (white% - draw% - black%):
(1.410x) 6... Nge7 (24% - 45% - 32%)
(370x) 6... d6 (20% - 34% - 45%)
(6x) 6... d5 (17% - 50% - 33%)
which makes my wonder if castling is really the best option there, even being the most played
This is the continuation my stockfish recommended, in response to e6 striking in the center with d4 -> cxd4 -> Nb5
This for e6, obviously. But what about a normal developing move like Nf6? Very conventional, huh? Well... Book move! Next book move is d4! But theres something rather interesting with Nf6:
According to professional matches database, here is the win rate:
(1.942x) 6... O-O (34% - 48% - 18%)
(867x) 6... d4 (47% - 38% - 15%)
(67x) 6... d3 (21% - 48% - 31%)
Obviously this is good for white, which is our main topic here. But since it might change in a near future, thats worth talking about.
Im not a professional, neither a good player. This thread is to get opinions and thoughts about the best approach (not necessarily a engine line) of winning agaisnt the ultra-symmetrical variation of the english opening, the most common continuation of 2... c5. Feel free to share your thoughts, no matter your ELO, i will take my time to analyze everything. Thanks for your time, peace.