In Firefox 109, Mozilla introduced a "unified extensions button". Normally, you can fully customize your toolbar, but this button cannot be moved or removed from the toolbar via the usual "Customize Toolbar" method.
However, it can be removed with an edit to your Firefox config. To remove it, open
about:config. There is a boolean setting
extensions.unifiedExtensions.enabled that defaults to true. Change it to false, restart Firefox, and you shouldn't see it in your
Hopefully Firefox makes it normally customizable in the future, like every other item on the toolbar.
Thanks to "Unified extensions toolbar button" in this Reddit post.