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I can see from your screenshots that Windows is detecting your iPod Classic as a disk drive, which is actually a good sign. It means the hardware connection is working fine. The issue is most likely related to how Windows 11 handles the iPod with iTunes.
Here are a few things you should check:
First, make sure you have the latest version of iTunes installed from the Microsoft Store. Windows 11 sometimes has issues with older iTunes versions. Go to the Microsoft Store, search for iTunes, and install or update it.
Second, the iPod Classic is being recognized as a disk drive, which means you can actually use it in disk mode without iTunes. Open File Explorer and you should see the iPod appear there. You can drag and drop music files directly onto it if you want to use it that way.
Third, if iTunes is not seeing the iPod, try these steps: Disconnect the iPod, open iTunes, then reconnect the iPod. Sometimes iTunes needs to be open before you plug in the device. Also check if you see the iPod icon in the top left corner of iTunes near the play/pause button.
Fourth, if the iPod still does not show up in iTunes, try right clicking on the Apple iPod USB Device in Device Manager, select Update Driver, then choose Browse my computer and Let me pick from a list. You might want to try selecting a generic USB Mass Storage driver instead of the Microsoft one.
Fifth, if you are using a USB hub, try plugging the iPod directly into a USB port on your PC. Some hubs do not provide enough power for the iPod Classic.
Also since you did not describe what specific problem you are having, could you let me know what is not working? Is it that iTunes does not recognize the iPod, or you cannot transfer files, or something else? That would help narrow it down.
Let me know how it goes!