<p>Employing the Hirota method, this work investigates a (3+1)-dimensional Kairat-X-type equation for the fluid-related nonlinear dynamics. Based on the bilinear form in the reported literature, a type of the bilinear Bäcklund transformation and a Lax pair are built. Under some parameter conditions, we explore the fission/fusion solutions and breather solutions. Moreover, we construct the hybrid solutions composed of the breathers and solitons, which represent the interaction between/among the periodic breather waves and localized solitons. To present the plane and spatial structures of those solutions, we generate the 2D and 3D graphical visualizations. Those figures demonstrate the plane and spatial structures of the fission/fusion waves, the periodic oscillation patterns of the breathers, and the elastic interaction process between/among the breathers and solitons. This study might enrich the understanding of nonlinear phenomena described by the (3+1)-dimensional Kairat-X-type equation, e.g., those in fluid dynamics. Additionally, the methods employed in this work could serve as a reference for investigating other higher-dimensional nonlinear partial differential equations.</p>