When energy is converted into mass...?

That is a question which physicists have been puzzling over for decades.  (And if I knew, I wouldn't tell you until I'd collected my Nobel Prize!)

E.g. see this: https://home.cern/science/physics/matter-antimatte...

Not sure where you're getting your information from, but converting energy into mass does not produce equal parts matter and antimatter. Antimatter annihilates when coming into contact with matter, so if your assertion were true, it would be an endless cycle of energy converting to matter and antimatter, the two meeting and cancelling each other out, producing pure energy again