Good thing we already have all of these!
For magic tridents, we have the "Trident of Dark Tides," a powerful type of weapon you can find on your adventures, similar to Gunpowder Barrels. They fire bubbles of energy which explode on impact; the longer you charge the bubble the more damage it deals, but the slower it moves. It's really good for clearing out PvE threats, like Skeletons or Ocean Crawlers, and for smashing Siren Statues.
We also have sunken temples: Siren Shrines and Treasuries. These are marked on the map, and are easily seen from your ship by the swirling lights coming up from the waves. Dive down, and swim all the way to the sea floor to find and enter them, then solve the puzzles inside for treasure! You can even store treasure you find in special statues down there, which you can then recover when you return to your ship. You might even find a Coral Message in a Bottle on your adventures, which will direct you to one of these temples to find a valuable treasure called the "Breath of the Sea."