The custom header links is a pretty simple theme component and I think it would be a good start to use the same code base but to put the link list somewhere else.
That said, it doesn’t support submenus, which would be tricker to add.
Another approach would be to do a component without any settings, just using HTML, CSS (and maybe a bit of JS). So, it would be a pretty “static” customization and if you need to do any change, you’d have to edit the proper HTML and CSS code.
Here’s an example I made for my own forum:
And how it looks in the site customizations:
Would such a way suffice for your needs, or do you prefer something easier to edit from the admin side like the custom header links component with several inputs, like this?