The stress-energy (or in the case of the Schwartzchild solution, the mass) is the source of the curvature.
Can you then explain the vacuum solution Schwarzschild solution where T=0? Or any other non-flat vacuum solution? Schwarzschild does not require mass...
Just as the electric charge is not the same thing as the electromagnetic field, but is the source of the electromagnetic field,
This is what I was trying to explain: they are VERY different theories. Maxwell is linear, where-as GR is non-linear. In Maxwell, the field is charge-less and hence does not self-interact. In non-linear theories, the fields also carry charge: gluons have colour, W and Z carry Hypercharge... and gravity gravitates.
the stress-energy/mass is not the curvature, but is the source of the curvature.
True, but you have to understand that curvature is also a source of curvature. You do not need stress-energy to get curvature.
However, gravitational waves are generated only in the case of dynamic solutions.
True, you need a quadrupole moment to generate gravitational waves. But that is irrelevant to the discussion regarding curvature generating curavture. The Kerr solution is another vacuum solution.
Also, gravitons are not only related to dynamic solutions and gravitational waves. They are also the quantum element of static solutions.