I suggest finding a plugin that does this and using it as guidance towards your own efforts.
I don’t know for sure, but I suspect such a plugin uses JS to replace the default textarea with a rich text editor. There is no useful hook to directly do this server side, but you could use the “{$taxonomy}_edit_form_fields” action hook to call wp_editor() while ensuring the added editor uses the correct name attribute and is wrapped in appropriate HTML table tags. The editor will appear below the default textarea. You’d need JS to remove the default one so only the WP editor remains.
