The stress-energy tensor is part of the Einstein Field Equations that describe space time. Solving these equations for real examples, in order to calculate the effects of mass, energy, etc can be complicated. In many cases there is no analytical solution so you have to use an approximation or a simulation. For some cases there are exact solutions: black holes of various types, a universe with homogeneous distribution of mass, and others.
The source of the curvature of spacetime and thus gravity in General Relativity is the stress-energy tensor"?
Your next post says that you wrer okay with my longer explanation..
The point is whether we can find a center-of-momentum frame or not, which is an inertial frame in which the energy of the system is minimized, which provides us with an invariant notion of "mass". So for a lump of matter, the center-of-momentum frame is the one attached to its center of mass, and the mass equals its rest mass. For a bottle filled with a hot gas, and thus consisting of many molecules bouncing around chaotically, the mass is not the sum of the rest masses of the molecules, but the total energy (rest mass + kinetic energy) in the frame in which that quantity is minimized (which will usually be the frame in which the bottle is stationary).
Going to the photon arrangements, for a single photon (or many such photons) all travelling in a single direction, it is obvious that no center-of-momentum frame exists. The energy of the photon in any frame is proportional to its frequency. So suppose we randomly pick a frame and it has a certain frequency. We can then choose a frame that's moving in the direction of the photon relative to our first frame, and due to the doppler shift the frequency (and thus energy) will be lower. But we can keep doing that ad infinitum, so there doesn't exist a center-of-momentum frame (and if we'd define it as the limit of our frame-shifting process, the limit would be zero energy anyway). This is of course also true for two or more beams of light all going in the same direction. If we have at least one photon that is going in another direction (such as two opposite directional beams), we can define a center-of-momentum frame in which the system will have non-zero energy. And that energy is then the invariant mass of our system of photons and a source for their mutual gravitational attraction. We should note that the source of gravity is the stress-energy, not the invariant mass per se, but it does work out that way in this case.