BingSearchEnabled registry setting breaks my non-web search

The problem is linked to update KB4512941.

Microsoft say they will repair it mid-September.

https://support.microsoft.com/en-us/help/4512941/windows-10-update-kb4512941

When I set BingSearchEnabled = 0 in registry Windows search stops working. When I set BingSearchEnabled = 1 Windows search works again but includes web search which I do not want. It's also worth noting that when BingSearchEnabled = 0 the process SearchUI.exe is constantly running at about 32% CPU.

This is a known issue with KB4512941.

Windows Desktop Search may not return any results and may have high CPU usage Microsoft is getting reports that a small number of users may not receive results when using Windows Desktop Search and may see high CPU usage from SearchUI.exe when searching after installing KB4512941. This issue is only encountered on devices in which searching the web from Windows Desktop Search has been disabled.

Microsoft plans to patch this problem in September 2019.

We are working on a resolution and estimate a solution will be available in mid-September.

Source: Windows 10, version 1903 and Windows Server, version 1903

How do I make Windows search work without having web search enabled?

If you don't feel like waiting, for a fix to be released, I would revert back to KB4512508 (18362.295) by uninstalling KB4512941 (18362.329). In the end, the actions you have taken should have disabled the web searches and allowed local searches to work, without causing high CPU issues with SearchUI.exe.