Firefox already has a Responsive Design Mode [0] that does this, but for one pane. Combine that with a tiling window manager and you get everything except the pane mirroring without having to use a proprietary browser.
I'd be interested in knowing if any other solutions exist just to add in the syncing functionality.
Edit: a comment mentioned Browsersync [1]. Browsersync + a proper window manager should give you everything Polypane offers and more, with any browser.
[0]: https://developer.mozilla.org/en-US/docs/Tools/Responsive_De...