⚠ This addon extends and works only with Tree Style Tab. This extension allows you to click on a tab in Tree Style Tab's sidebar to unload it. You can set conditions for which clicks will be used. It is also possible to block Tree Style Tab's default action for a click. Conditions for clicks:

Hold certain modifier keys while making the click. (Such as: ctrl, shift, alt, meta/command.)
Tab is/isn't double clicked.
Tab is/isn't long-pressed.
Tab is/isn't long pressed without tab being dragged. (special event from Tree Style Tab's API.)

If the tab that should be unloaded is the current tab then you can control what tab should be selected instead with the following options:

Select the last focused tab instead of the closest.
Ignore hidden tabs.

Context menu items that can be added to the context menu in Tree Style Tab's Sidebar:

Unload tab.
Unload tree.
Unload tree descendants.
Unload other tabs.

The context menu items can be added after a slight delay to ensure that they are the last items in the menu. If there are more than one item they will be grouped under a parent item. This extension can also:

allow keyboard shortcuts to unload tab/tree (requires Firefox 60 or later).
Dim unloaded tabs in the Tree Style Tab Sidebar.
Hide all unloaded tabs so that they aren't visible in the toolbar and can't be selected with keyboard shortcuts. Hidden tabs are also not selected when you close the current tab. Useful to prevent accidental loading of unloaded tabs.
Show hidden tabs in the Tree Style Tab Sidebar. Useful when combined with the option to hide unloaded tabs.
Fix some bugs with Firefox unload method. For example tabs that aren't restore correctly after being unloaded by an extension or tabs that are marked by Firefox as loaded when they are unloaded. These fixes work for other tabs that are unloaded by other extensions as well. (This is a workaround for a Firefox bug that is fixed as of Firefox 62.)
Unload tabs via the Auto Tab Discard extension. (Can be useful to change the icon of unloaded tabs)

When using the default configuration:

Hold the alt key and click tabs to unload them.
Middle click on loaded tabs to unload them. (Not possible in Tree Style Tab v2.4.18 or earlier.) (Also you can double middle click or middle click while holding a modifier key to close tabs that can't be unloaded, such as addon option pages.)
Hold a modifier key and right click tabs to unload them.
Unloaded tabs are dimmed.
Unload tab context menu item in Tree Style Tab Sidebar context menu.

Note that all functionality is fully customizable in the options page.