Methods and systems are provided for exhaust flow in an engine system including a split-exhaust manifold for expediting exhaust catalyst light-off and engine warm-up while reducing condensation in the engine system. In one example, a method may include, before exhaust catalyst light-off, flowing all or more exhaust gases, via a first exhaust valve and a first exhaust manifold, to an exhaust catalyst by passing a heat exchanger. Further, after light-off but before engine coolant warms up to a threshold temperature, all or more exhaust may be delivered to the heat exchanger, via a second exhaust valve and a second different manifold, prior to flowing to the exhaust catalyst; and exhaust gas recirculation may not be provided until the coolant reaches the threshold temperature to reduce condensation.