CNN — Top aides to President Joe Biden have embarked on outreach campaigns they hope will help make his handling of the Israel-Hamas war a defining element of his presidency — and his campaign for a second term, particularly if contrasted with likely 2024 rival Donald Trump. These aides and others who have spoken with the president since Hamas first launched its attack on Israel say Biden sees the conflict and the US response to it as part of the battle for the soul of America, just as he sees his presidency. He has brushed away calls, including from an…