Energy in physics feels analogous to money in economics. Is a manmade medium of exchange used for convenience. It is the exchange medium between measureable physical states/things.
Is energy is real in the same way money is? An incredibly useful accounting trick that is used so frequently it feels fundamental, but really it’s just a mathmatical convenience?
Small aside: From this perspective ‘conservatipn of energy’ is a redundant statement. Of course energy must be conserved or else the equations are wrong. The definition of energy is it’s conservation.
The matter does get converted into those photons.
Said another way:
The things go from being a couple of spin-half particles/antiparticles to a flurry of spin-one photons.