The growing interests and applications of graph learning in diverse domains have propelled the development of a unified model generalizing well across different graphs and tasks, known as the Graph Foundation Model (GFM). Existing research has leveraged text-attributed graphs (TAGs) to tackle the heterogeneity in node features among graphs. However, they primarily focus on homogeneous TAGs (HoTAGs), leaving heterogeneous TAGs (HeTAGs), where multiple types of nodes/edges reside, underexplored. To enhance the capabilities and applications of GFM, we introduce H$^2$GFM, a novel framework designed to generalize across both HoTAGs and HeTAGs. Our model projects diverse meta-relations among graphs under a unified textual space, and employs a context encoding to capture spatial and higher-order semantic relationships. To achieve robust node representations, we propose a novel context-adaptive graph transformer (CGT), effectively capturing information from both context neighbors and their relationships. Furthermore, we employ a mixture of CGT experts to capture the heterogeneity in structural patterns among graph types. Comprehensive experiments on a wide range of HoTAGs and HeTAGs as well as learning scenarios demonstrate the effectiveness of our model.