Your face normals are inverted. You can see the faces in blue when they are correctly pointing outwards when you check Face Orientation under Overlays. Go tab into Edit Mode and press 3 to switch to Face Select mode then press A to select all faces.
Then go to Mesh > Normals > Recalculate Outside or press the shortcut Shift+N
Now the face normals are blue and correct and you can add the Subdivision Surface modifier