This is based on a papercut: https://devtalk.blender.org/t/more-sculpt-modes-for-the-shift-left-mouse-hotkey/10048
The problem is clear: Insufficient brush options to momentary switch brush via shortcut without leaving the active brush
Actually we just give support to smooth, invert brush and normal brush effect. Some of the most - ask for - options/brushes to be included in this menu are: mask brush, brushes that flatten the surface such as scrape and flatten brushes, and so.
With this patch I give support to add brushes by type to the 'Stroke Mode' list as well as mask brush tool. Extend the list from this point is pretty easy as only few lines per brush have to be added. I also took in count the shared across property between texture paint and sculpt so I splitted it to be able to extend the property for sculpt while maintaining the one from the texture paint giving then more possibilities for the future to expand them independently without any problem.
Also, this patch has a reduced version of the list with just few needed brushes. But I have a patch that includes almost all brushes just in case core devs agree with it. From user feedback I got that everyone want to have the freedom to choose any brush, that is, to have the complete list of brushes. That's why I think could be positive to include all them on the list.
I have made a reduced build to test the patch: https://blender.community/c/graphicall/7jbbbc/