Manifold Solidify
By default, when extruding a planar mesh (such as a grid or filled curve), the bottom is left open, resulting in incorrect topology.
To properly solidify a mesh, flip the faces of the original geometry, and join it with the extruded geometry. Merge by distance afterwards to weld them together.
Advanced Technique: Offset
Using some math, you can offset the original geometry along the face normals. The setup above will replicate the offset of the solidify modifier.