I'm Greg, an installation specialist and 8 year Windows MVP, here to help you.
On the View tab of Device Manager, choose Show Hidden Devices. If the phone isn't being recognized I'd uninstall the driver and restart PC to reinstall.
If that doesn't help, from Action tab choose Scan for hardware changes.
There are enough problems with phones and other devices being recognized via USB in Windows that for iPhone I'd use a superior backup method which is iCloud wirelessly in the background: https://support.apple.com/en-us/HT201391
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.