Math behind L2 Regularization for Logistic Regression I read that L2 regularization in logistic regression creates a sort of sphere that limits the choice of $w$ weight, but why does this happen?
Your question is really about the method of Lagrange multipliers in constrained optimization, not logistic regression per se. The gist of it is that a constrained optimization problem can be recast as an unconstrained optimization problem by adding a term, called the regularizer, and vice versa. The sphere comes from recasting the unconstrained problem into a constrained one; recall that a constant $L_2$ norm defines a hypersphere.