Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional (1D) systems, but introducing additional spatial dimensions is generally expected to destabilize them or destroy their coherent character. Here we experimentally investigate how deep-water gravity-wave solitons behave when diffractive spreading along the transverse direction is introduced in a controlled manner. Using a large-scale water-wave facility, we generate solitonic wave packets whose transverse structure is imposed across a segmented wavemaker through either a sharp slit or a smooth Gaussian apodization. The resulting two-dimensional wave fields are measured with high spatial resolution. We find that diffraction strongly reshapes the transverse structure of the wave packet while its longitudinal dynamics retain clear signatures of soliton coherence. Numerical simulations based on the hyperbolic nonlinear Schrödinger equation accurately reproduce the experimental evolution. Furthermore, nonlinear spectral analysis based on the inverse scattering transform reveals the persistence of soliton dynamics over a significant portion of the wave field. At the same time, the measured transverse profiles are quantitatively described by classical diffraction theory over a broad range of conditions. These results provide an experimental characterization of how coherent structures inherited from an integrable 1D system evolve under controlled departures from one-dimensionality, revealing the robustness of soliton dynamics in the presence of transverse diffraction.