How can i bake this stylized generator into a base color ?

Hello @Tudor36232527wfk4,

The stylized filter uses the layerstack underneath to compute the stylization, therefore the Base Color is based on your layer stack.

To export your Base Color, make sure to use an export preset that contains a Base Color channel. Hopefully most (if not all) do contain a Base Color.
https://helpx.adobe.com/substance-3d-painter/getting-started/export/creating-export-presets.html

For baking the environment lights in the Base Color, there's a filter named Baked Lighting Environment. You'll need to plug the HDRI map in the filter, but it will work as expected.

Best regards,