What does the black dot next to my iPhone 15 Dynamic Island mean?

I found this possible answer to your question:

The black dot on your iPhone is likely due to Assistive Touch being enabled, a software feature. If it's Assistive Touch, you can turn it off in Accessibility settings. 

That's the front camera.

It's likely associated with an app you have on your iPhone, which may be running in the background.

Can you tap the black circle? Does it open anything if you tap it?

You could swipe up from the home bar slowly, halfway up your screen to bring up the app switcher, and slide any apps you haven't fully closed one by one to see if the circle goes away.

You could also Force Restart your iPhone, which may make it go away --> Force restart iPhone - Apple Support

Those are the new privacy indicators introduced in iOS 18.4. They’re supposed to display an orange or green dot beside the Dynamic Island to represent the microphone and/or camera is being used by an application. I would try the Forced Restart lobsterghost1 suggested as it probably just bugged.