"melden" is more used if you report a small issue, like to report a bug or to to report spam juat to let someone know it happened. "sich melden" is to raise your hand in school and "sich freiwillig melden" is to volunteer. "berichten" is more to give a report which is usually more detailed. Like to give a report about an event that happened or any kind of news. But in the news there is for example "Eilmeldung" which is breaking news or like very new news. In this case you usually also expect them to be very short and not so detailed.
I hope that helped.
I will report this for the thousand time. German speakers in the exercises are terrible. The sound of their voice is not properly recorded and creates blank spaces in the sounding. Here the word "melden" sounds like "mel". His voice is too bass to record exercises. I mean we got that he is a man, he doesnt have to show gis masculinity speaking like selling a car. GET REAL PEOPLE DUO TO RECORD GERMAN. NO SHOW OFFS...
I think the 'n' is pronounced, but it's very nasal and the 'e' pretty much disappears, which makes it very hard to distinguish. I've often noticed this with words that end 'en'...
EDIT: I just came across 'Das werden wir beachten' and again the 'en' on both verb parts is swallowed up. I still think the 'n' is pronounced though.