Pro contains more goodies, but it does not unlock functionality. You do not have to buy Zorin OS for it to work. Choosign Zorin OS pro is a way to Support Development.
This is odd... Your output shows:
*-network UNCLAIMED
description: Network controller
But also shows your ethernet as well as wireless:
*-network
description: Wireless interface
capabilities: ethernet physical wireless
configuration: broadcast=yes driver=rtl88XXau driverversion=5.13.0-28-generic ip=192.168.68.111 multicast=yes wireless=IEEE 802.11bgn
It shows the driver in use.
Your system output shows:
00:14.3 Network controller [0280]: Intel Corporation Device [8086:7af0] (rev 11)
DeviceName: Onboard - Ethernet
Subsystem: Intel Corporation Device [8086:0074]
Kernel modules: iwlwifi
Did you modprobe your wireless driver?