When you right-click an app icon, or just blank space on the taskbar, the relevant context menus will pop up faster. This ought to speed up right-clicking on the Taskbar. In the Performance Options window, unselect the ‘Animations in Taskbar’ option, and click Apply.
In the System Properties window, go to the Advanced tab and under the Performance section, click ‘Settings…’ If for reasons known only to Microsoft you can’t get this to work, right-click on This PC and select ‘Properties’ instead. In the window that opens, select ‘Advanced system settings’ from the left bar. Right-click on the Start menu and select ‘System’ from the context-menu. Specifically, this is meant to make right-clicking on the taskbar much faster so that jumplists and the taskbar’s own context menu pops up faster than it normally does. If you’re one of the lucky few who aren’t plagued with the problem being persistent but still have a slow-to-respond Taskbar then there’s a simple fix you can apply. For some, the problem is persistent and renders the Start menu impossible to use whereas for others, it comes and goes. A lot of users running Windows 10 are having problems with the Taskbar not being responsive, or the Start menu delaying too much before it opens.