@Josr Hi and welcome to ther forum.
Can you tell us more about the hardware you have Z16 Core running on?
especially: Processor, RAM, WiFi card/device.
Does WiFi show up when you use Zorin USB in "Try Zorin" mode?
In the Zorin Software Updater app settings, check that it is pointing to "Main Server", not a local server. You can also do a check for additional drivers whilst in there.
Can you please open a terminal (ctrl + alt + T) and run
lshw -c network
Post the results here.
There seem to be one or two simlar instances of this on the forum. e.g. No wifi icon in taskbar Zorin 16 Core