There is no reason why a CSS rule placed on the page will not affect the HTML on that page. This is the way to style the HTML area and I advise you open a support ticket where you can attach a video and a sample that showcases the issue.
The ContentAreaCssFile needs to add a <link> element in the document of the editable <iframe> used in Design and Preview modes, which is a separate context, but the HTML mode <textarea> is in the main document.
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