I think you mean the Toolbox icon. That’s the one that has all the Tool icons on it.
The Toolbars have things like opacity sliders and the brush editor icon on them. They can have Tool icons on them as well if you configure them and add the icon of your choice. There are so many icons you can put on a Toolbar.
There are five Toolbars and all are configurable. If you Unlock the Toolbars by doing
Settings → disable Lock Toolbars, then you can see the grab handles for each Toolbar then you can position them individually adjacent to the main application window boundary, either in horizontal or vertical orientation.
See example: Tips and Tricks - Hidden Gems in Krita - #37 by AhabGreybeard
There are two usually empty toolbars, Custom toolbar 1 and Custom toolbar 2.
Those can be unlocked (see above) and placed top/bottom/left/right at the edges of the main window and have any icon that you like on them.
Given that mainToolBar and editToolBar usually have only five icons between them, you can transfer those icons to the BrushesAndStuff Toolbar to give two more empty toolbars that could be used as custom toolbars. It’s a deep rabbit hole 