I've encountered the same issue and the Windows Update Troubleshooter fixed it.
Maybe you can also have a try.
This article may help: https://www.drivethelife.com/windows-10/fix-windows-update-error-80070666.html
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Error Code 80070666 just popped up when I tried to install important update, how do I fix this?
<Original title - Windows update >
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I've encountered the same issue and the Windows Update Troubleshooter fixed it.
Maybe you can also have a try.
This article may help: https://www.drivethelife.com/windows-10/fix-windows-update-error-80070666.html