Computer Configuration > Administrative Templates > Microsoft Edge - Default Settings (users can override)
Both
HKLM\Software\Policies\Microsoft\Edge\Recommended
Enables Windows to index Microsoft Edge browsing data stored locally on the user's device and allows users to find and launch previously stored browsing data directly from Windows features such as the search box on the taskbar in Windows. If you enable this policy or don't configure it, Microsoft Edge will publish local browsing data to the Windows Indexer. If you disable this policy, Microsoft Edge will not share data to the Windows Indexer. Note that if you disable this policy, Microsoft Edge will remove the data shared with Windows on the device and stop sharing any new browsing data.