but what got me was Connor writing "I have made a mistake"(or something along those lines) under Haytham's portrait after his death.

There's a cut dialogue line where, in their final encounter, first Connor once more asks Haytham to break the cycle of violence with him, then finally begs for Haytham's life, but both times Haytham rebuffed him ("breaking the cycle of violence = fantasy" and them being mortal enemies) having his mind set on at least one of them dying... if those lines had been included, I might have wondered if Connor had written that phrase under Haytham's portrait out of regret that he didn't get to know Haytham more before killing him (I very much got "either you kill me or I WILL kill you" from Haytham's cut line), or that he in the end couldn't persuade Haytham.