This is a difficult question even for an experienced blender user. I haven’t seen widespread use of custom menu bars. A quick search for an answer comes down to using non-standard scripts to create such menus. I’m not sure that such solutions will be acceptable now and compatible with future versions of Blender. Here is a similar description https://b3d.interplanety.org/en/creating-custom-tool-in-blender/. But perhaps not everything is so bad and there is a standard solution, about which I unfortunately cannot say anything.
The documentation includes the following explanation: “The Quick Favorites menu gathers your favorite tools. Any tool or menu item can be added to this pop-up menu via its context menu.” That is, to add to favorites, you need to click on the required tool button and call up the contextual menu and execute “Add to Quick Favorites”. The item will be added to favorites, which can be viewed by calling the {Q} key.
The tool bar menu has the same tools as the toolbar panel (t-panel T)… (see for example the 3D-viewport in object or edit mode or the UV-editor… ). The later (panel) can be changed to display on or two rows… or one row with text…
The already given reply is somekind of irritating (compatibility and bad ???) because the given link perfectly describes how to change the menu/panel… but it just doesn’t show (directly how to make an addon out of this…
(Some addons for example also add “buttons” to the toolbar…)
Copy and paste this script into Blender’s text editor and run it. This script defines a simple tool that adds a cube when you click in the 3D View. You can modify the execute method in the SimpleOperator class to perform any other action you want.