How can I theme individual fields in a row?
You are on the wrong track. If you want to rewrite in twig how the fields are built to a row, you have to use the template views-view-fields.html.twig.

But the simplest method would be to rewrite the result of the fields in views ui. This is the option "Override the output of this field with custom text". If you apply this on the last field and hide all previous fields with the option "Exclude from display", you can see the twig variables for all fields in "Replacement patterns" and you are able to rewrite the complete row like the example you have shown in the question.