And it always plays this ominous music when approaching their prey.

More relevantly, the fossil records for sharks are mostly their teeth and jaws, because all their other bones are cartilage and rarely fossilize.

"Sharks haven't significantly evolved in appearance in 350 million years" is therefore based on reconstructions made under the assumption that the old sharks mostly looked like current sharks, which may or may not be true.

Though we can get a surprising amount of information that way, for example one change is that their jaws used be more at the end of their snout instead of more underslung like today, like so:

https://www.smithsonianmag.com/science-nature/new-technologies-reveal-strange-jaws-prehistoric-sharks-180977396

You'll note the Goblin Shark still has hints of that design.

I made sure to say barely instead of not at all, but you're right, there was certainly some evolution happening

Yes, actually. Example: Triglidae

They are bottom-dwelling fish, living down to 200 m (660 ft), although they can be found in much shallower water. Most species are around 30 to 40 cm (12 to 16 in) in length. They have an unusually solid skull, and many species also possess armored plates on their bodies. Another distinctive feature is the presence of a "drumming muscle" that makes sounds by beating against the swim bladder