userChrome.css: Floating collapsible sidebar for vertical tabs. Video demo: https://youtu.be/bonasv2q98U

userChrome.css

@-moz-document url("chrome://browser/content/browser.xhtml") {

  /* To bring back OS title bar with min/max/close buttons, some users might
   * consider setting browser.tabs.drawInTitlebar to false in about:config
   */
  :root {
    --custom-sidebar-collapsed-width: 35px;
    --custom-sidebar-full-width: 20vw;
    --custom-sidebar-border: 0px solid #404040;
  }

  #TabsToolbar {
    visibility: collapse !important;
  }

  #navigator-toolbox {
    border-bottom: 0 !important;
    background-color: var(--toolbar-bgcolor) !important;
  }

  #browser {
    position: relative;
  }

  #sidebar-box:not([hidden]) {
    position: absolute;
    z-index: calc(var(--browser-area-z-index-tabbox, 0) + 1);
    display: flex;
    flex-direction: column;
    overflow: hidden;
    border-right: var(--custom-sidebar-border);
    min-width: var(--custom-sidebar-collapsed-width) !important;
    width: var(--custom-sidebar-collapsed-width) !important;
    height: 100%;
    transition: all 0.2s ease;
  }

  #sidebar-box:hover,
  #sidebar-box.hovered,
  #sidebar-header,
  #sidebar {
    width: var(--custom-sidebar-full-width) !important;
  }

  #sidebar {
    flex-grow: 1;
  }

  #sidebar-splitter {
    display: none;
  }

  #sidebar-box:not([hidden]) ~ #tabbrowser-tabbox {
    margin-left: var(--custom-sidebar-collapsed-width) !important;
  }

  #sidebar-box:not([hidden]) ~ #tabbrowser-tabbox .findbar-container {
    min-width: calc(100vw - 48px - var(--custom-sidebar-collapsed-width)) !important;
  }

  /* Sidebar on the right */
  #sidebar-box[positionend="true"]:not([hidden]) {
    right: 0;
  }

  #sidebar-box[positionend="true"]:not([hidden]) ~ #tabbrowser-tabbox {
    margin-left: 0 !important;
    margin-right: var(--custom-sidebar-collapsed-width) !important;
    border-right: 0;
    border-left: var(--custom-sidebar-border);
  }

  /* Full screen */
  #main-window[inFullscreen][inDOMFullscreen] #browser > #tabbrowser-tabbox {
    margin-left: 0 !important;
    margin-right: 0 !important;
  }

  /* Place sidebar header at the bottom */
  /*
  #sidebar-box:not([hidden]) {
    flex-direction: column-reverse;
  }
  */
  
  /* Collapsible sidebar header
   * works best when positioned at the bottom
   */
  /*
  #sidebar-header {
    border: 0 !important;
    padding: 0 !important;
    height: 1px;
    opacity: 0;
  }
  
  #sidebar-header:hover {
    padding: 8px !important;
    height: auto;
    opacity: 1;
  }
  */
  
  /* Hide sidebar header */
  /*
  #sidebar-header {
    display: none;
  }
  */
}

New version with no need to manually calculate top panel heights. This CSS now works out of the box, no configuration required.

@Froggy232 and @GrigorijST , see this gist for FF 107 sidebar auto-shrinking fix

Thanks you A LOT!
It works flawlessly without configurations, that's the best userChrome.css that I have tried, thanks you again

I'm trying to use this userChrome.css script, and it's really great! I'm unable to move tabs around and rearrange them inside the same panel, because as soon as I click and start dragging a tab, the sidebar collapses completely. I can move tabs from one panel to another, but not within the same panel. What would you recommend?

@NinjaTuna007 seems like this is no longer a problem on FF 132

* btw updated gist to support FF 132 layout changes
** updated to support FF 138 layout changes