If you want full Side by side browsing mode:
Some part of it is extremely easy - to display ALL tabs side by side:
profile/chrome/userChrome.css :
tabpanels {
display: -moz-box !important;
}
tabpanels > notificationbox {
-moz-box-flex: 1;
border-width: 2px !important;
border:solid #888;
}
For the other part - to have only two panels, sibling is easy, otherwise you would need some JS to mark a tab as something like content-secondary and handle it (e.g. there was an extension last_selected_tab doing like this AFAIR) - as you have only: tabpanels > notificationbox > browser[type=content-primary]
(Just tested in Firefox 60.4.0.esr - newer versions may need some minor adjustements in CSS, toolkit.legacyUserProfileCustomizations.stylesheets preference set to true and probably some other fixes. In 2008 I had a Norton Commander 'clone' made in such incredibly simple way, ALL file and media formats preview (plugins), with a bit of custom code for nsIProtocolHandler, and nsIURIFixup fixes :) , kudos to archView extension by Pike/Solar Flare.)R.I.P. Firefox.
I can already have two pages next to each other using Windows 10, by snapping two windows to the two sides of the screen. However, while that provides the correct visual shape, the user experience is completely different, as clicking a link in the left window will not open that page in the right window, replacing what's already there.
https://mozilla.crowdicity.com/post/728459 says about Side by side browsing mode which I see as: with any two tabs, the content of the default active/content-primary tab will be replaced by link clicked on the other visible tab.
Again something that used to work in Firefox.
FWIW: I use Tree Style Tabs (or Sideberry) to see why I arrived at a page. Not exactly the thing specified here but it works today.
Yeeep, I used it for a while: https://archive.is/ovRDX (addon no longer exists, it broke with Firefox Quantum)