Demand for kindergarten seats in the Boston public schools for this fall has risen by more than 25 percent, an unanticipated increase that has left hundreds of students without an assigned school and has prompted school officials to add more classrooms. The boom surfaced in the past few months during the first round of registration for kindergarten classrooms that will serve students who will be 5 by Sept. 1. The School Department received 2,306 such applications, up from 1,823 during that same period last year.