Shortcuts for Firefox tab groups

Does Firefox have any keyboard shortcuts related to tab groups, like creating a new group, moving a group left or right, collapsing or expanding it, etc.?

There are no direct shortcuts to interact with tab groups. The list of shortcuts can be seen in this Firefox help page.

However, you can still interact with tab groups via the keyboard only. It is not very convenient but still an option if mouse interactions are undesirable for any reason. The main point is in the Selection of Multiple Tabs section:

These shortcuts require the tab bar to be “in focus”. Currently, the only way to do this is to focus an adjacent object and “tab into” the tab bar, for instance, by hitting Ctrl + L to focus the address bar, and then Shift + Tab repeatedly until the current tab gets a colored border.

This does appear to be the easiest way to focus the tab UI components. Recap:

To start, you have to focus the URL bar (Ctrl+L or Alt+D or F6. When the dedicated search bar is disabled the following also work: Ctrl+K or Ctrl+E) or the search bar (if enabled: Ctrl+K or Ctrl+E) then cycle through the browser UI elements with Shift+Tab until you reach the tabs.
Note this will not cycle through each tab. If you miss the component, press Tab to cycle in the opposite direction.

Once you do that you can navigate through tabs by pressing Down/Right to go highlight forward through tabs Up/Left for backwards.

• To expand/collapse a group: highlight it and press Space which toggles between the states.
  Note: you have to highlight the tab group name to collapse it:

  

  not on a tab inside the group

  

• Once you have highlighted a tab, you can press the Menu key on the keyboard (or Shift+F10) and do operations like add it to a group, or remove it from a group via the menu. Use Up/Down to go through the options and select one with Up/Left and select with Enter or use the underlined letters in the menu to directly trigger that menu item (e.g. for "Remove from Group" press "R").

  • To select multiple tabs: hold Ctrl then cycle through the tabs with the arrow keys and press Ctrl+Space (you should still be holding Ctrl, so technically just tap Space for each selection). Once you have them selected, you can do bulk operations via the context menu, like adding all to a group or removing from a group.

• Once you have highlighted a tab group, you can press the Menu key on the keyboard (or Shift+F10) to interact with it. You have to cycle through the menu with Tab to move between the name field, the colour options, and the options for the group. Confirm a selection using Space or Enter.