There is a way to configure the Start11v2 context menu, but it involves making some Stardock provided changes in the Registry, and a change in the Windows Settings>Personalization>Colors.

Are you running Windows 10 or 11?

Are you using the Enhanced Taskbar?

I'm not exactly sure how you are getting the context (or flyout) menu color in your screenshot. The default for this menu is a translucent black.

To change the Context (Flyout) menu color:

Open RegEdit (Win+R and then type regedit and hit enter).

Navigate to  HKEY_CURRENT_USER\SOFTWARE\Stardock\Start8\Start8.ini\Start8

Right Click the Start8 Key and select New>String Value

Name it:  S11_MenuStyle

Now right click this new string and select Modify

In the resulting dialog enter 2 for the Value Data

Close RegEdit and then Restart Explorer for the change to take effect.

The Value Data has 3 options:

0 = translucent menus;
1 = solid menus;
2 = color tinted translucent menus

You can select the highlight color for this menu in Start11 as follows:

Now open The Windows settings and navigate to Personalization>Colors and scroll down to "Show accent color on Start and Taskbar" and turn it on, and then select the color you want to make the background of the Context (Flyout) menu.

NOTE: This wont affect the Start menu or the taskbar choices you made in start11. It will change the color of the Windows Notification menu, the highlight color for buttons in settings, and the bar underneath the app in focus on the taskbar.

Example: Seafoam color chosen in System Settings and blue chosen in Start11 "Selected item accent color."

Good luck! Let me know if you have any questions.

Great! Happy to help.