First, to directly answer the question posed, no there is no direct migration path as the two tools are different, are configured differently, and have different capabilities all of which you must arbitrate per your requirements. "Your requirements" is always key when moving from one system to another, simply translating (or attempting to translate) the actual knobs, switches, bells and whistles from one to another is rarely a recipe for success even if possible on the surface. The configuration in system is the realization of your requirements and not the requirements themselves. Thus, you always need to take a step back to what your requirements are (and define them if you never have) and then translate those into the capabilities of the new system.
Next, there is no Windows Server management in Intune (and there are no plans to ever add this either). Server OS management from the cloud is part of Azure ARC: https://learn.microsoft.com/en-us/azure/azure-arc/overview.
Finally, yes, there technically is an agent for Intune, but this is (more or less) built into each of the managed OSes. The entire point of MDM is to use the built-in management capabilities of the managed OS instead of the MDM itself having to create its own management stack. Intune does supplement the built in management stack on Windows though using a separate agent called the Intune Management Extension (IME). The IME builds on top of and extend some capabilities of the built-in Windows MDM stack; the IME is automatically installed on Intune enrolled Windows endpoints and for most intents and purposes, is completely transparent to the end user and Intune admin.