Spin-charge interconversion provides the essential link between spin information and electrical signals in spintronic devices. In spin-orbit coupled systems, spin-charge interconversion can contain multiple components associated with different spin-polarization directions, reflecting the underlying spin texture. Tuning this spin texture therefore provides a way to control not only the magnitude of spin-charge interconversion, but also the balance among its different components. Graphene-based van der Waals heterostructures provide an attractive platform for this purpose because interfacial spin-orbit coupling can host multiple spin-charge interconversion channels that couple to different spin-polarization directions. Here, we demonstrate electric-field control of spin texture in a dual-gated HfS₂/graphene van der Waals heterostructure, where independent control of carrier density and vertical electric field allows us to disentangle electrostatic doping from electric field-induced spin-orbit effects. Nonlocal spin precession measurements show that near zero vertical electric field, spin-charge interconversion is dominated by a spin Hall component with out-of-plane spins. Increasing the vertical electric field enhances additional in-plane spin components with Rashba-Edelstein-like character, including both parallel and perpendicular to the charge current contributions. These results provide experimental evidence that a vertical electric field can reconfigure the effective spin texture and control the corresponding spin-charge interconversion components, demonstrating electrical tunability of spin-orbit functionalities.