I understand your question but their is nothing wrong here. I hope this will help you , this is Because when you preview your template then it shows the initial value of the CSS property which is set in the theme but when you change the color from content editor then the initial value gets updated on the page level not at theme level. So it doesn't matter which color you choose for you button in content editor, it will not change the initial value in theme.
Hope this will helps you out. Please mark it as Solution Accepted & Upvote to help other Community member. Thanks!
I don't need the preview, design manager or theme link because to open those links I would need access of your portal. Please provide the page link for that you need to publish the page and in settings you will find that page url. If by any reason you are unable to publish the page then you can Book a meeting and me or my team will help you out.