Methods and systems are provided for operating a split exhaust engine system that provides blowthrough air and exhaust gas recirculation to an intake passage via a first exhaust manifold and exhaust gas to an exhaust passage via a second exhaust manifold. In one example, while both a first exhaust valve and second exhaust valve of a cylinder are open, intake air may be routed through a flow passage coupled between the intake passage and the first exhaust manifold, the first exhaust manifold coupled to the first exhaust valve. The intake air may be further routed through the first exhaust valve, into the cylinder, and out of the second exhaust valve to the second exhaust manifold coupled to the exhaust passage including a turbine.