Does relativistic mass affect space time in the same way as rest mass?

To my understanding, (as I am not an actual physicist, but simply a citizen scientist) relativistic mass is really the measure of an object's energy. It is not the same as rest mass, which is the definition of mass that a layperson would be familiar with (how much matter an object is composed of). However, does a change in relativistic mass amount to the same magnitude of gravitational variation as an equivalent change in rest mass?

(On a related note) If so, why are objects not affected by gravity generated from photons, which have relativistic mass?

Does relativistic mass affect space time in the same way as rest mass?

To my understanding, (as I am not an actual physicist, but simply a citizen scientist) relativistic mass is really the measure of an object's energy. It is not the same as rest mass, which is the definition of mass that a layperson would be familiar with (how much matter an object is composed of). However, does a change in relativistic mass amount to the same magnitude of gravitational variation as an equivalent change in rest mass?