I used to have a widget area that looks like the demo:
Somehow through fixing other errors on my site I have lost it. When I try to set it up again it looks very different, with the widgets stacked vertically on top of each other instead of in a row. I'm currently trying to create it via appearance/customize. Do I just have to play around with the settings more to make it look like the demo, or am I on the wrong track?
In Theme Options -> Header & Menu settings, the Classic Header Widget area should be turned on. Here are the settings as on the demo:
However you don't need to use the Icon with text widget here, You can also use any other widget as well. If you want to use multiple widgets, then I recommend adding a Layout builder widget first, add a row inside with as many cells as you require, then add your widgets into those cells
The Layout builder widget will give you full control of how widgets are displayed and it'll make sure, all the header widget area elements are stacked horizontally on desktop ( not one below the other).
I hope this helps,