Is there anything like Tabs Outliner but attached to the same window? More like Tree Style Tabs. At this point I may even be willing to run mitmproxy to inject an iframe into every page or something :(
This is not quite what you asked for, but you can achieve a "managed dual/side pane" with a tiling window manager, letting the window manager keep the outline on the side rather than the browser, so that you don't have to juggle windows yourself. I do this with Tabs Outliner myself and it's quite flexible for me: when I want a full screen vs a side panel, I simply switch between the layouts.