It's a must have! Thanks.

It's just the Firefox 57 upgrade that is a bit hard but it is not the developer's fault! I was just surprised not to see my vertical tabs on the left (even after some FF restarts) until I read that there is a button to display it! Maybe there is a bug or the developer simply forgot to make this visible by default or maybe FF57 does not allow this.

For the upgrade, I had to follow the migration tutorial here: https://github.com/piroor/treestyletab/wiki/How-to-convert-session-information-from-old-TST-0.19.x-to-new-TST-2.x
And then I used the following CSS rule to hide the "standard tab bar on the top": https://github.com/piroor/treestyletab/wiki/Code-snippets-for-custom-style-rules#hide-horizontal-tabs-at-the-top-of-the-window-1349
First I had to created a folder chrome inside my user profile directory, then a new file userChrome.css where I placed the following code:
#TabsToolbar {
visibility: collapse !important;
}
This hides the "standard tab bar on the top" as expected.
Now I finally have TST quite as before, and at least as usefull as before!

Thanks again @Piro and other developers to keep maintaining this add-on!