Systems and methods for a split exhaust engine system

An engine operating method, comprising:

• flowing blowdown gas without blowthrough air from a cylinder of an engine to a first and a second exhaust emissions devices via a blowdown exhaust valve and a blowdown manifold coupled to the blowdown exhaust valve during a cycle of the cylinder, the second exhaust emissions device downstream of the first exhaust emissions device;
• and
• flowing an amount of blowthrough air from the cylinder to the second exhaust emissions device and not the first exhaust emissions device via a scavenge exhaust valve and scavenge manifold coupled to the scavenge exhaust valve during the cycle;
• where the blowdown manifold is a first exhaust manifold in fluidic communication with a plurality of engine cylinders and a turbocharger turbine;
• where the scavenge manifold is a second exhaust manifold in direct fluidic communication with the plurality of engine cylinders and an inlet of the second exhaust emissions device;
• and
• adjusting an amount of overlap between opening of the scavenge exhaust valve and opening of an intake valve of the cylinder to adjust the amount of blowthrough air in response to an air-fuel ratio of gases in the scavenge manifold.