That's the way. Easy as pie.
Thank you for your answer, but I still didn't quite understand, what is the way.
Do you mean, that there's no other way to do that but to select the whole text in the text box?
It the text frame (not box!!!!!) is threaded you have either to select all text frames at once in the thread (which is impossible if they are on different spreads) or you have to select the whole text to apply a style.
If the text frame is not threaded, you can select and apply the text.
I see not a problem in selecting all text. Use the text tool, click into the text and cmd/ctrl+A and apply the style. Not a problem, not a lot of work.
A box is something like the BleedBox, CropBox or something like this. Objects in InDesign are always frames or paths.
Thank you for your answer.