This is not an issue with DEVONthink.
What you’re seeing in the ChatGPT app is styled HTML, not rich text. And it copies as raw Markdown. There is no style information included.
Actually ChatGPT.app copies plain text, rich text and HTML but not Markdown to the clipboard. And pasting this into a rich text document or an HTML page works indeed as expected over here (of course the styling is different).