The AskHistorians booklist has plenty of good recommendations - you're looking for the Ancient Near East under the Middle East. Links to the booklist can be kinda funky for me, but hopefully it works: https://www.reddit.com/r/AskHistorians/wiki/books/middleeast/#wiki_ancient_near_east/

The Ancient Near East: A Very Short Introduction by Amanda Podany is a great intro. It's short and inexpensive, and gives a broad overview of the region up until Cyrus the Great. Sumerians are only part of that history but they get a lot of attention.

A History of the Ancient Near East by Marc Van De Mieroop is the de facto standard for a more detailed introduction of the ancient near east. Again, Sumer is only a piece of this. This is pretty readable as far as textbooks go but you still might want to read the very short introduction book first to make sure you're interested.

For Sumer specifically they mention a few works by Harriet Crawford but those are a little more expensive and/or harder to find so you might want to go with the cheaper introduction first to make sure you're that interested.

Early Mesopotamia: Society and Economy at the Dawn of History by J. N. Postgate is a classic too, focused on early Mesopotamia, but be aware it's getting old now.

I'm not familiar with the YouTube channel, and looking through past posts I don't see anyone successfully getting an answer about it. I would guess given that the series is named Fall of Civilizations that it might have an interest in making things seem more cataclysmic when in reality things are usually more complex and more nuanced, which is what I would keep in mind watching it. One problem with ancient history is that since the finer details are scarce time is usually dealt with in bigger blocks. It's easy to forget that (just for example) 50 years or so is a long time, a couple of generations really, when you're always reading about hundreds of years here and there.