interesting. i have had the emperor angel ever since he was a baby. grew from 1 inch to about 5 inches in 5 years. i have a 75 gallon. only him a hippo tang and 3 damsels. all fish are very active and the emperor was always the boss of the tank. recovered from popeye but still mopey and no appetite. hides in rocks all the time now. this was not gradual, very sudden.
There are a few possibilities for this behavior.
I used to raise my marine Angels in my 75 gal as well. I would take babies and grow them up for a few years then trade them in for small ones again. If this is not your intention, you should know that at 5", your Emp is getting a bit too large for your tank. Be aware that if this is the case, the rest of possibilities won't fix the problem
Another possibility is that the popeye came as a result of an injury caused by another fish in the tank. If this is the case and the offending fish is still present, this may be the cause of the moping.
Since you treated with Amoxicillin, you need to be checking your ammonia/ nitrite levels as Amox is an antibiotic and may have disturbed the biological filter causing your water parameters to now be off. Testing the water before doing water changes will let you know if this is the case.
Popeye, unfortunately, is also a symptom of Ichthyphonus with listlessness being a second indicator. Sadly, this is a disease that is more easily prevented than cured. Fish under stress succumb to this internal fungal disease more frequently than people know. Since it is an internal issue and few medications are designed for internal problems, cure is hard to come by. If the fish is still eating, you may want to use a medicated food for bacterial/fungal issues. Another med is Maracyn 2(monocycline) which is designed for internal issues but keep in mind, it may already be too late for this fish if his organs are too effected. It is also recommended that infected fish be isolated in a qt/hospital tank as the infection is spread through the feces and fish coming into contact with infected feces will more than likely also get infected.
I would eliminate these possibilities in order (from top to bottom) as the top ones are easily fixable.
Hopefully , one of those is the case
I hope this helps