Hi Eric,
In my - documented (by guides/plugins) - journey to learn TW5 I started already in the alpha phase of TW5.
It's a very long time ago (January 2014) I made (in TW 5.06beta) the first version of a 'Top + Left menu' (the 'Top menu' is a direct spinoff of that 'Top + Left menu').
It was a design decision to use a tagpill-based top menu (at that time it was the easiest way to get a top menu).
The restriction is that the submenu entries are only links to tiddlers. In most cases that is no problem; in your case it is. The only workaround I see is creating tiddlers with an iframe to the site you want to display. Something like:
But be aware: not all sites can be displayed in an iframe.
May be TonyM's menu plugin can be used better for your case.