When the reaction get colder in an endothermic reaction what has happened to the heat energy?

Why is a reaction endothermic ?
For a reaction in which the total enthalpy (heat content) of the reactants is lower than that of the products, energy should be absorbed for the conversion of low-enthalpy reactants to the high-enthalpy products. Therefore, the reaction is endothermic.

Heat flow for an endothermic reaction :
For an endothermic reaction, heat is absorbed from the surroundings to the reactants for their conversion to the products. The surroundings include the solvent of the reaction mixture and the reaction vessel. As heat is absorbed from the solvent of the reaction mixture and the reaction vessel, their temperatures drop and they feel colder than before the reaction.

The energy is being utilised in forming bonds between the atoms and/or molecules in the reaction (chemical energy).

When those bonds are broken you get an exothermic reaction, as the energy locked in the bonds is released.

the reaction doesn't get colder, the system does. Some heat energy gets converted into chemical (bond) energy.

Really, in a nonscientific explanation, it is kinetic energy (which is what temperature measures, total kinetic energy of the system), energy of motion of atoms and molecules being converted into glue energy, energy energy used for sticking together rather than bouncing and spinning around.