No. A majority of the tanks on here don’t use any bio filtration media. It is completely unnecessary (in most cases). That is why we have live rock! The only valid reason (IMO) to use bioballs or matrix is in certain tanks that for aesthetic reasons decided to have minimal or no rock work in the display tank, OR have a ridiculously high bioload/borderline overstocked with fish. Freshwater tanks are different, and this is often a hard concept to grasp for folks that transition to salt from fresh, but I promise you it is 100% not needed in your tank. Toss it in the garbage and watch your nitrates fall!
Carbon is also not necessary, though it is far more commonly used in the saltwater hobby. It helps with water clarity and can remove unwanted contaminants in an emergency, like “oops, I just put my hand in the tank after putting on sunscreen”. I run it for peace of mind mostly. Your tank will absolutely not “crash” without it.