Estimating heterogeneous survival treatment effects (HSTEs) from time-to-event data under time-varying treatments is important in fields such as medicine (e.g., to decide which sequence of treatments is better in terms of survival probability). However, this task is challenging because treatment decisions, patient characteristics, and censoring probability often evolve together, requiring sequential adjustment for both treatments and censoring. Existing survival learners mostly consider a single baseline treatment assignment, while longitudinal treatment-effect learners typically assume uncensored outcomes. In this paper, we introduce a novel doubly robust learner for heterogeneous survival treatment effects under time-varying treatments and history-dependent censoring. Our framework separates the intervention window from the survival horizon, with treatment prescribed for a finite period, after which care follows its natural course. We further establish the favorable theoretical properties of Neyman-orthogonality, rate double robustness and quasi-oracle efficiency. The framework accommodates flexible machine learning models for nuisance estimation and treatment-effect regression. We evaluate our learners through several numerical experiments, demonstrating their effectiveness.

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