Added a clarification
After I had spent several hours trying to get the physics export to work using the method described in this chapter combined with the "better collada exporter" I finally understood that there is a plugin that is called Godot-Blender-Exporter.
Since it used to be the default to use the "better collada exporter" I didn't understand that the title of the page is a name, not a description. After all the better collada exporter is kind of a godot to blender exporter.