To add to this, there were a few cool XUL-based software out there back in the day: Songbird, ActiveState Komodo IDE, Zotero, etc. XUL didn't take over the world like Electron, but for a moment it felt like it could.
And yes you could absolutely do a Matroshka with it: a VB6 app embedding Internet Explorer and the site embedding an ActiveX element written in VB6. Or inline Java applets.
Funny times... an era in which security was barely a concern. Instead, you had open-ish, usually well documented interfaces for everything.
What killed the idea though until Electron came along was simple: Browsers didn't even come close to feature parity. You had to write your own API layer to communicate between the website and the host application for everything going beyond XHR calls and file selector uploads. Electron took off once Chrome got enough native bridges that you could actually write capable web apps.