The Dodgers-Giants rivalry has new life, and a backup catcher is responsible. Dalton Rushing is single-handedly reviving what has felt like a dormant divisional antagonism between the teams. Over the past three days, the second-year catcher has sparked controversy, been thrown at, and authored a dirty slide. He’s on a roll and has injected energy into a rivalry that had been a bit quiet while also coming across as completely unlikable. On Tuesday night, Rushing was the endpoint of a relay that resulted in San Francisco’s Jung Hoo Lee being tagged out at home. As Lee remained on the ground, apparently injured, cameras caught L.A.’s catcher being dismissive of the injury. He claims that wasn't the case , and later checked in to make sure Lee was O.K. In the top of the sixth inning on Thursday, Giants starter Logan Webb hit Rushing with a fastball into the ribs, then walked toward him. — KNBR (@KNBR) April 23, 2026 Rushing kept his head down and took his base, but there was some more bad behavior coming.…