That is incorrect. Photons have mass. They have no rest mass. They also cannot rest, so you might wonder how relevant that is.

The concepts of rest mass and relativistic mass are considered outdated. In modern physics, "mass" means what they meant by "rest mass".

Here some indication I'm not making this up: https://hsm.stackexchange.com/questions/2465/when-and-why-di...

In any case, I never use those concepts, and I know no professional particle physicist that does. By "mass", I mean rest mass.

When you put a photon in a stationary box, the "relativistic mass" of the photon becomes part of the "rest mass" of the photon-box system. You can't ignore it.