Exactly why is energy released when a bond is formed?
is this applicable to both ionic and covalent bonds?

Energy is released when bonds are formed because bonds are more stable and require less energy.it takes energy to get divorced, it but it is much easier (requires less energy) to stay together.
The amount of energy required to break the bond is called bond energy, and the total change in energy is called enthalpy. If the reactants have strong bonds but the products are weak, it is called an endothermic reaction and the energy required to break the bonds is greater than the energy released. But if the reactants have weak bonds and the products have strong bonds, it is an exothermic reaction. In this case less energy is needed to break the bond and more is released when strong bonds are formed. This is a negative enthalpy change - meaning the system released energy.