Note: there’s a limited version of this feature already available. If you select an existing piece of text and then leave it selected while you use the Text tool to create new text, its style will match the piece of text you had selected.
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Note on the _limited_version of the feature described above...
You have to select the "area text" box, not the text itself, Copy it (CMD+C), THEN you can can use the type tool to create new text with that copied style.