I was curious of the feature, so I went to Variable Text in LightBurn - LightBurn Software Documentation page.
I did something similar, including the choice of Merge/CSV you didn’t mention but ednisley mentions.
When I click and maintain the click on the Test button, I see the change of %0 with the value in the CSV file.
When I look at the Preview, the change is effective too.
Perhaps you missed a step?
Note: in the above page, perhaps it would be clearer to mention that the “Variable Text window” is actually (by default) a tab in the same location than Cuts / Layers?