Is there a way to copy the HTML out of an Outlook email?

the problem here is that styled text in Outlook is not always sent as HTML.

But you can find out easily enough. (Note this works on Outlook 2016. other versions might be different.)

Hold down the ⌥ Option key on your keyboard and click on the message in Outlook's message list that you want to see the source for and select "Show Source" from the menu that pops-up.

If it was sent as HTML you will see the HTML code. But a lot of people use what outlook calls "Rich Text" which embeds the email as an '.rtf" document. Which is fine as far as it goes as Rich Text Format is a standard that most word processors can read and write (like the macOS textedit.app).

So some (if not many or most) of your emails won't be in HTML format at all.