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;
  }
  */
}

@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