In this work, we address this gap by introducing a novel form of conditional cross-fitting adapted to the dependence arising in survey sampling. Leveraging this approach, we develop a unified theory for the asymptotic behavior of model-assisted estimators based on general prediction methods. In particular, we establish the asymptotic normality of the proposed estimators and the consistency of a corresponding cross-fitting variance estimator, thereby enabling the construction of asymptotically valid confidence intervals. The proposed approach is shown to be asymptotically optimal in that it reaches the Godambe-Joshi lower bound. Simulation studies further demonstrate the favorable finite-sample performance of the proposed methodology.