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SurveyJS
Open-Source JSON Form Builder to Create Dynamic Forms Right in Your App. With SurveyJS form UI libraries, you can build and style forms in a fully-integrated drag & drop form builder, render them in your JS app, and store form submission data in any backend, inc. PHP, ASP.NET Core, and Node.js.
I strongly recommend using the SugarCube story format, since it's flexible and has the most built-in tools of any of the default Twine story formats. In the SugarCube "CSS" documentation section, it shows you how you can change backgrounds using tags you set in your passages and CSS you put in your Stylesheet section. Also, if you really want to have your own UI in SugarCube, you can use the StoryInterface special passage to change the layout however you want (though this will take knowing a bit of HTML and CSS).