This did not happen in the previous versions of Sketchup. We are using dynamic components to toggle the visibility of this geometry, just like we had been with previous versions.
The style in your SketchUp model has Profiles on and set to 3 which seems pretty heavy to me. I changed them to 1 and updated the model. This is what I see in LayOut:
If you don’t see the same thing, you might want to look at the OpenGL settings in Sketchup under Preferences>OpenGL.
I do see a couple of other issues that although they don’t directly impact the answer to your question, will cause you problems later. First, you aren’t using scenes in your SketchUp model. Instead you are using Last saved SketchUp view. This means if you go back to the SketchUp model and make any changes, changes in the camera position will transfer to the viewport. The other thing is you should NOT be copying and pasting from SketchUp to LayOut. That results in a separate reference SKP file for each viewport. You can see there are four SKP files in your LO file. And because you’ve are copied and pasted, the references become embedded meaning the viewports are no longer referencing the original model. Editing that original model won’t affect the model shown in the LayOut file.
Instead you should be creating scenes to show the model they way you want it in the document. Then you should either use File>Send to LayOut in SketchUp or File>Insert in LayOut to get the first viewport on the page. After that you copy and paste that viewport within LayOut to create the additional ones and in the SketchUp Model panel you choose the desired scene for each viewport.
By “previous” you mean which version?
The behaviour of hidden geometry in scenes in SketchUp has been changed. SketchUp now remembers the hidden status of subcomponents or groups per scene. You should save your SketchUp view that looks like you would like it to look as a scene, and use the Send to LayOut command to insert your model into your LayOut file. Once there, you should set your LayOut viewport to refer to the scene you saved. Especially, copying and pasting is not to be recommended. It creates a file reference to a temporary file.