A Computer-Aided Design (CAD)-native Bayesian optimisation framework for expensive three-dimensional computational fluid dynamics (CFD) problems is presented, enabling true multi-objective optimisation in mixed discrete-continuous design spaces under industrial manufacturability constraints. Bayesian optimisation has demonstrated strong potential for global CFD shape optimisation by efficiently exploring continuous geometric parameter spaces using surrogate models. In parallel, parametric CAD models have been integrated into automated CFD workflows to enable iterative geometry updates. However, most existing approaches are restricted to continuous shape variations within a fixed CAD topology, limiting their ability to explore design spaces involving discrete topological changes. The proposed framework enables both shape optimisation and parametric topology optimisation directly at the CAD level by embedding discrete design variables into the parametric model. Topological variation is introduced through discrete CAD design variables controlling the number of pin-fins in the streamwise and spanwise directions in a pin-fin cold-plate geometry. Continuous variables govern geometric dimensions, while additional discrete design variables define admissible feature orientations. Manufacturability is enforced by construction through admissible combinations of discrete and continuous CAD design variables, ensuring that each candidate design corresponds to a valid CAD geometry. The framework is demonstrated on an industrially relevant three-dimensional conjugate heat transfer pin-fin cold-plate problem formulated as a true multi-objective optimisation problem. Pressure drop and maximum temperature are minimised simultaneously, resulting in a Pareto-optimal front. Bayesian optimisation efficiently explores the mixed discrete–continuous design space, converging to a stable and meaningful Pareto front within approximately seventy CFD evaluations. The generality of the framework is further demonstrated on a separate single-objective shape optimisation case. The discrete nature of the design space enables non-smooth topological changes between optimisation iterations, which lie outside the scope of conventional gradient-based and shape-only optimisation approaches.