1. Press Windows Key + R to open the Run prompt. Type regedit and hit Enter.
2. Navigate to the following registry path:
   HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Search
3. Right-click the empty space in the right pane. Select New followed by DWORD (32-bit) Value.
   Set its name to BingSearchEnabled. Set the value to 0.
4. Restart your PC for the changes to take effect.
   And that's it. Your Start menu will now only search locally.

If you're on Windows 11 version 24H2 or newer running the May 2020 Update or later, there's an alternative registry path that you might need to update. Navigate to:

HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\Explorer
Create a DWORD called DisableSearchBoxSuggestions and set its value to 1 using the same steps mentioned above. This disables both web results and search box suggestions in one shot.