I’ve just re-read the last line of this paragraph. Freud is saying the depressed person feels low self-esteem but not shame:

Finally, it must strike us that after all the melancholic does not behave in quite the same way as a person who is crushed by remorse and self-reproach in a normal fashion. Feelings of shame in front of other people, which would more than anything characterize this latter condition, are lacking in the melancholic, or at least they are not prominent in him. One might emphasize the presence in him of an almost opposite trait of insistent communicativeness which finds satisfaction in self-exposure.

One of the things about depression is that it casts a dark shadow over ones perception of life. If any event can be interpreted in a negative way, depression does. It is one of the self-perpetuating aspects to depression that it sees everything in a negative light and then looks for justification to prove its’ validity. I wonder if that communication of negative self-esteem that Freud is talking about is a function of the self-perpetuating downward spiral of depression. Almost like how one might keep repeating something to establish it and believe it intentionally like an affirmation. Depression naturally reinforces itself in a downward spiral by believing negative things about oneself, then reinforcing that belief by repeating them.