Hi,
Azure Update management Center (Preview) is the latest service to be able to patch servers. For servers located outside of Azure you can use Azure Arc for servers to have the same functionality you have for Azure servers. You can create schedules to apply updates to apply specific categories of updates. Update management Center provides single pane of glass on updates across multiple servers no matter if they are located in Azure or outside of it. On reporting you will have to make something custom to query the data and e-mail the results. Azure offers different kind of services for automation like Azure Automation, Logic App or Functions. You can also check Azure Update Management which works in similar way, but it requires creating Azure Automation and Log Analytics resources. Azure Update management Center (Preview) will replace Azure Update Management at some point but currently missing some features that are available in the latter service.
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.