As Governor Charlie Baker laid out a state budget plan that attempted to rein in state spending across the board this week, he made an exception for the beleaguered Department of Children and Families: an increase of $30.5 million, which would finance 280 new jobs to help the state’s most vulnerable children. Advocates quickly expressed support. “Governor Baker has yet again shown his steadfast commitment to protecting the children of the Commonwealth,’’ said the Children’s League of Massachusetts. For an agency that typically makes headlines when tragedy strikes, it was a welcomed change of pace.