Reinhardt Flender: Hebrew Psalmody a Structural Investigation, for an overview of Psalm cantillation among Jews of North Africa and the near east.
...And for an understanding of how to recognize the signs, https://drive.google.com/drive/folders/12jzK6S9HojcCzTf4BOy8XEcD3NrO28WA
It's an Ashkenazi book, so forgive his ignorance of Sephardi and Yemenite practice. But nearly everything he has to say theoretically about the te'amim of the 21 and 3 books is pretty spot-on. You will simply have to substitute his melodic examples and speculations. There is also the issue that non-Ashkenazi psalm-cantillation can use a verse-melody... a kind of semi-improvisational or stock tune that is recited over words with minor te'amim.
But the performance practice of Psalm cantillation is at once simple and subtle and very deep and complicated. I've spent some time trying to understand the underpinnings of the various traditions, albeit as an aside to my main focus of assembling a database of melodies for the 21 books. Isaac Treuherz Montague is far more adept on this topic than I am. But he hasn't published anything on it yet.
I recommend checking out an introduction that I wrote to the topic of Psalm-cantillation on Cambridge's Digital Bible Research forum:
But click here for a goodle doc version of the thread, if you don't want to have to sign up for their forum: