The soil looks wet for the "rex". I would repot it to a much smaller pot with a fast draining mix to speed up recovery.

Angel wings like more water than other begonias.

Angel wings (canes) and most all begonias like water when they need it. Not overly wet but not dry either. There are exceptions though to any "rule" as some begonias are more succulent than others, therefore require less watering.

Yeah, the pot does look kind of big.