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, in response to flowing the exhaust gas recirculation and blowthrough air from the first exhaust manifold to the intake passage via a first set of exhaust valves, a first set of swirl valves coupled upstream of a first set of intake valves may be adjusted to at least partially block intake air flow to the first set of intake valves. Each engine cylinder may include two intake valves including one of the first set of intake valves and two exhaust valves.