I can't get a simple answer to this simple question online, so I thought I'd ask here.

Thermal radiation is usually meant to be the energy associated with a given temperature of a material body. Now certain radiation called thermal radiation can be assigned a well-defined temperature as well. Thus, it seems it seems that the energy of the radiation should be counted as thermal energy.

Is this true or not or is this a matter of semantics because the tern "thermal energy" is underspecified?

Suppose I have a blackbody in an isolated room with perfect reflector walls. Say the body has $3\text{ J}$ of thermal energy (as the sum of kinetic energies of the particles wrt the rest frame of the object/room) and the blackbody radiation surrounding the body (in equilibrium) has $6\text{ J}$ of radiation energy. What is the total thermal energy of the isolated room?