Message "The software required for communicating with iPods is not installed." on a loop

My laptop runs the 64-bit version of Windows 10 and all of my system software is up-to-date. I recently updated iTunes to the app version Windows users are now encouraged to obtain from the Microsoft store, version 12.9.3.3. I have a 160 GB iPod Classic that I connect using a cord I know to be good as it is the same cord I use to hook-in to my car for listening to my iPod. I have verified that the iPod's drivers are current and I have run the diagnostic tests suggested by another thread in this forum and there are no indications that the iPod is corrupted.

Since updating to the latest iTunes version, every time I connect the iPod, the message appears, "The software required for communicating with iPods is not installed. Would you like to download and install it now?" I have clicked on "Download and Install" and the icon appears for the download in the same area as downloading purchases from the iTunes store appears. A message then appears to state it is installing iPod Support. However, nothing happens after that message disappears. If I close iTunes and re-open, or disconnect and re-connect the iPod, the same message appears. I have read other posts and ensured that the iPod Support service is set to Automatic, and stopped and restarted the service as directed.

I even went so far as to remove the latest app version, reinstall an old desktop version, and my iPod was once again recognized. However, the software was then running very slowly and I prefer to be able to run the most current version of the iTunes software. When I re-updated to the app version and once again attempted to install the iPod Support software, I actually clicked on the .exe outside of iTunes to attempt to more fully install and it highlighted that I needed to remove some of the components related to the older version of iTunes. Even after doing this, it still gives me the same message about the required software not being installed.

To summarize, I have read several posts and explored all remedies put forth in these support forums and have now exhausted all of my options. There is nothing wrong with my hardware, cords, or system software, and I have no viruses or malware. This appears to be solely an issue with the new app version of iTunes for Windows and the associated iPod Support software. Please help me resolve this frustrating loop and inability to sync my iPod Classic. Thank you.