Your very old first generation iPad mini can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).
Apple ended update support for iPad mini in September 2016. The iPad mini1 cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed - in addition to which, iPad mini is a 32-bit architecture device, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms.
iTunes should recognise the iPad. Ensure that you have updated iTunes to the most recent version. If still experiencing connection issues, this support page may be help:
https://support.apple.com/en-us/HT204095
As an alternative, have you considered using iCloud for the backup? This backup can be used to restore data to a new iPad.
I hope this information and additional guidance might prove to be helpful.