You could change the text area to a text column and make it pushing.
To change it to a text column select it in the text tool and drag the bottom right handle up to the top right handle. Hold CTRL down to constraint the width.
To make it pushing select it in the selector tool, right click and select "Position on page / Push..." and check the Push option. You might need to disable the lock button...

But this will not make the green rectangle grow automatically. You could use a text panel if you would like that to happen.