Two claims that are simply false

The Prophet, peace be upon him, was never sad. This gets said often and it is contradicted by the report you just read, and by the year of the seerah that carries sorrow in its name.

And the other one. If you prayed properly you would not feel this way. That converts a symptom into evidence of religious failure, and its measurable effect is that people hide. A person who believes their illness is a verdict on their faith does not tell anyone about it, and not telling anyone is how this gets worse.