This phase III trial tests whether adding trastuzumab and hyaluronidase-oysk (Herceptin Hylecta [TM]) or pertuzumab, trastuzumab and hyaluronidase-zzxf (Phesgo [TM]) to the usual chemotherapy (paclitaxel and carboplatin) works to shrink tumors in patients with HER2 p...