Illustrator: Edit text in multiple text boxes at the same time

You can dynamically load text into Illustrator using an XML file.

Using the Variables panel, you can import an XML file and use that to
control the existence of objects, what images appear in linked image
containers, and what text appears in a text frame. You can also
control the data that appears in a graph. The typical workflow is to
create a template document and then tag it for variables.

There are multiple tutorials online discussing how to do this. This article: HOW TO USE ADOBE ILLUSTRATOR VARIABLE DATA WITH XML has a good video and step by step tutorial on how to do this.

Or you can do either of the following:

1) Delete the second text box. Make the text change. Copy -> paste text and apply the font or character style.

or

2) Just copy the text and paste into the other text box after finishing editing the first text box.