This phase II trial studies the immunologic response and side effects of using the WOKVAC vaccine in combination with chemotherapy and HER2-targeted monoclonal antibody therapy before surgery in treating patients with breast cancer. Vaccines like WOKVAC are made from tumor-associated antigens which may help the body build an effective immune response to kill tumor cells. Chemotherapy drugs, such as paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Trastuzumab and pertuzumab are forms of targeted therapy because they work by attaching themselves to specific molecules (receptors) on the surface of tumor cells, known as HER2 receptors. When trastuzumab and pertuzumab attach to HER2 receptors, the signals that tell the cells to grow are blocked and the tumor cell may be marked for destruction by the body's immune system. Giving the WOKVAC vaccine at the same time (concurrently) with paclitaxel, trastuzumab, and pertuzumab before surgery may kill more tumor cells.