Specifically, I am inquiring about using the model on a website that serves as a showcase without any advertisements or commercial activities. Can anyone provide guidance on whether this is permissible and how to go about using the model on the website? Thank you for your assistance.
You need to get advice from actual legal counsel for this. None of us are in a position to officially interpret the EULA for you and the SketchUp staff people aren’t permitted to make that interpretation for you.
Without seeing your web site I would guess that you’d be OK with it if you are just showing what you are modeling in your hobby but you’d better get the advice from someone who is in a position to give it. Of course it might be less expensive to pay for a subscription to SketchUp GO than to pay a lawyer. There’d be no issue using images of your SketchUp models then.
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One possibility would be to upload to SketchFab. If I recall, you can then embed a link to display in your webpage.
Except that doesn’t change whether or not the OP’s use of the SketchUp file is permissable under the EULA.
Absolutely. I can’t speak to that.