Guttenburg and Classic Editor – How to use the custom guttenburg block in classic editor?

I would suggest you to provide your custom blocks with an additional plugin. You can add it automatically. If your users ever change their theme again, they won’t be able to edit their content anymore.
As mentioned in the comments, block features belong to the block editor. Your users should know that. They decide proactively to disclaim the block editor.

In cases as simple as your example button block you can provide a shortcode. If you want it badly 😉

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