After two weeks of quarantining, the coral beauty started eating pellet foods and even started responding to some training: I tap the tank gently ten times with the cap if the food container right before feeding. Also, I noticed a white spot on its fin during the second week, and did a freshwater dip to clear that away. Overall, my first attempt at quarantining was useful.
When I added the coral beauty to the display tank, the drama began. First, it some how got caught in the net. I thought it was its gills at first and fins, but after gently loosening the net around the fish, it appeared the fish was actually biting the net and not letting go. So it took about five minutes of some careful shaking, and eventually it released the net, but only after it was nearly unconscious. It sank immediately to the bottom if the tank. It lay there for a little while, but finally came around and started swimming slowly.
The yellow tang immediately swam up to it and began brushing up against it. I realized that it was wielding its blade, which was quite worrisome. I read that the coral beauty should be one of the first species to introduce and the yellow tang the last because it is more territorial, but I didn't plan well enough in advance. I'm hoping the coral beauty is hardy enough to avoid the tang. I may ads some more live rock to the tank as well.
On the second day, I was happy to see the coral beauty chase down some pellets during feeding time. And after hiding much of the first day, it has been exploring the tank much more, nibbling at the live rock. The tang still takes swipes at it every now and then, but the coral beauty, which is currently the same size of the tang, seems capable of avoiding it. There seems to be a slight discoloration/faded color in the scales of the coral beauty on the left side near its tail, which might be from the yellow tang's blade. The coral beauty is swimming around fine, though, so hopefully it's not serious.