TST will be possible with WebExtensions. For hard evidence, even the Add-Ons Engineering Manager is working on his own, personal vertical tabs webextension to suss out what APIs we need: https://github.com/andymckay/sidebar-tabs
We may not land everything we need by the time Firefox 57 releases, but we'll get there. If we miss, you have options: you can decamp to Firefox ESR for a few months, where TST will keep working, or someone could theoretically convert TST to a WebExtension Experiment which would work on DevEdition and Nightly builds of Firefox.
That's very good news. TST is one of the few things that makes web browsing even vaguely viable these days.
I've noticed (on the rare instances I'm on desktop, mostly Mac these days) that Vimperator is also borked (only parts of it seem to be functioning). That's another lifesaver to me, and whatever it takes for it to come back to life and/or an alternative to provide effectively similar functionality ... would be peachy.
If I can lure you to another bit of developer / user advocacy, a bit from about 3 years ago on the content management problem:
We may not land everything we need by the time Firefox 57 releases, but we'll get there. If we miss, you have options: you can decamp to Firefox ESR for a few months, where TST will keep working, or someone could theoretically convert TST to a WebExtension Experiment which would work on DevEdition and Nightly builds of Firefox.