For example, I have a Patreon link on the header of my discourse, but it opens in the same tab. I’ve tried to look in settings for anything relevant, and there is something in user preferences, but even though it’s ticked on, still no external links open in a new tab.
Have you tried adding
target="_blank" to your link?
I’m using the header links plug-in, and here is the entry I have for Patreon, and, as you can see, I do have blank entered there, so it should be opening aa new tab. However, it is not
Try disabling plugins and theme components - I suspect you may have a conflict between the Custom Header Links component and something else.