Add an anchor link to a ‘plain’ HTML file, without over-writing the entire site?

Well this approach is not remotely close to the proper way to use WordPress, so there is just not going to be a correct way to do this. However the problem is that you’re linking directly to a file in the theme. This is incorrect. To create a page in WordPress you need to create a page under Pages and then link to that page’s permalink. If you need that page to use bar.html then you need to create a page template for that page that includes bar.html into it.