It looks like you have multiple copies of the Data Management Gateway installer on your C drive, and you are not able to find any evidence of the gateway being installed in your Programs and Features list or by using the Get-WmiObject cmdlet.
Here are a few things you can try to determine whether the Data Management Gateway is installed on your system:
Check the Services list in the Windows control panel. The Data Management Gateway installs a service called "Azure Data Management Gateway". If this service is listed and running, it means the Data Management Gateway is installed on your system.
Check the installation folder for the Data Management Gateway. The default installation path for the Data Management Gateway is C:\Program Files\Microsoft Azure Data Management Gateway. If this folder exists, it means the Data Management Gateway is installed on your system.
Check the registry for the Data Management Gateway. The Data Management Gateway installs several keys in the Windows registry under the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\DataManagementGateway key. If these keys are present, it means the Data Management Gateway is installed on your system.
Check the Event Viewer for any errors related to the Data Management Gateway. If the Data Management Gateway was installed and is not functioning correctly, it may log errors in the Event Viewer. Please share the same for verification
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