What to do with leftover broth from mussels - is it safe to reheat?

It should be safe. I would reboil to make sure. As for what to do with it, make soondubu (Korean tofu soup). Here's a recipe from my favorite Korean blogger:
https://www.maangchi.com/recipe/sundubu-jjigae

You can use the mussel broth in place of the anchovy/kelp stock is that often used in Korean cooking.