Uninstalling "Windows Web Experience Pack" using Powershell and reinstalling it from the Microsoft store fixed the issue for me:
- Open PowerShell as admin
- Type the following command and hit enter: winget uninstall "windows web experience pack"
- Type "Y" when prompted
- Reinstall the pack by grabbing it from the Microsoft Store: https://www.microsoft.com/store/productId/9MSSGKG348SP
- Go to taskbar settings, the Widgets switch should be there, disable it and enable it again
- That's it! Widgets icon should appear in your taskbar.