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, a method may include decreasing gas flow from the first exhaust manifold to the intake passage, upstream of a compressor, where a first set of exhaust valves are exclusively coupled to the first exhaust manifold, in response to a condition of the compressor. Further, the method may include increasing gas flow from the first exhaust manifold to an exhaust passage coupled to a second exhaust manifold coupled to a second set of exhaust valves, in response to the decreasing gas flow.