The second generation Apple Pencil will never be compatible with any of the pre-existing range of iPads - other than the 2018/2020 iPad Pro and the new iPad Air4. Future models of iPad may be designed to support the second generation Apple Pencil.
The first and second generation Pencil use an entirely different pairing and charging interface. The second generation Pencil can only be used with iPad models that have the magnetic/inductive dock that is exclusively designed for the Pencil. A software update cannot add electronic hardware that the iPad does not possess.
The first generation Apple Pencil, compatible with your iPad, uses the physical Lightning port for both pairing and charging the first generation Pencil. This pencil can only be used with compatible iPad models that have a Lightning connector.
In summary, the Apple Pencil models are not interchangeable - and can only be used with the iPad that has appropriate internal hardware.
Connect Apple Pencil with your iPad - Apple Support
Apple Pencil compatibility - Apple Support
If your are able, you should return the incompatible Pencil to your retailer - and seek an exchange for the correct model.
I hope this clarification is helpful to you.