If you like, you can say that the Einstein field equations define the active gravitational mass (or, more precisely, the active gravitational mass-energy-momentum-stress).
But active gravitational mass equals inertial and passive gravitational mass, so this makes the EFE more than a definition.
The EFE also contain all kinds of information that has nothing to do with sources. For example, they say that certain vacuum fields are not possible, and they predict the existence of gravitational waves.
There are some ambiguities that come into play in the case of dark energy.
The Einstein tensor $G$ is measurable. For example, when I drop a pencil and see how long it takes to hit the ground, I am finding out something about the Riemann tensor in a certain region of space. By doing enough measurements, I can measure the entire Riemann tensor and then determine $G$. This constitutes an operational definition of $G$. We could define $G$ in some other way, but we don't need to, it seems undesirable, and nobody does it.
The Einstein field equations relate the Einstein tensor to the stress-energy tensor. In the nonrelativistic limit, this is simply equivalent to the Newtonian equation $g=Gm_a/r^2$, which relates the active gravitational mass $m_a$ to the gravitational field. This can be taken as the definition of active gravitational mass in Newtonian physics, and there is no other way to define it. However, this does not make Newton's law of gravity a tautology or a definition, because in Newtonian gravity the active gravitational mass is strictly equal to both the passive gravitational mass and the inertial mass. Since we have other types of experiments that can measure inertial mass, there is no circularity involved. Furthermore, Newton's law of gravity specifies the distance dependence of the field, which is not a matter of definition. This $1/r^2$ form of the force law results, for example, in the prediction of elliptical orbits.
Similarly, in GR, the active gravitational mass (or, more precisely, active gravitational mass-energy-momentum-stress) is defined as $G/8\pi$, and there is no other way to define it. However, this does not make the Einstein field equations tautological or a matter of definition, for the same reasons as in the Newtonian theory.
Note that in GR, the equality of inertial, active, and passive gravitational masses is not just an optional feature as in Newtonian gravity. If any of these equalities fails, then GR is falsified and cannot be fixed by tinkering. (E.g., it's a theorem in GR that test particles follow geodesics.)
One place where I think it gets a little trickier to make proper operational definitions is in the case of dark energy. We have no way to measure the inertia or passive gravitational mass of dark energy. This is basically because our model of dark energy is a cosmological constant, and the Einstein field equations do not allow us to simply make solutions in which the cosmological constant varies from point to point. Such solutions always violate the field equations. Therefore the cosmological constant is ordinarily modeled as a constant -- it has no dynamics. (You can have a dynamical dark energy, but doing so requires something more elaborate than just letting $\Lambda$ vary.)
This lack of dynamics in $\Lambda$ prevents us from measuring dark energy's inertial or passive gravitational mass. For this reason, it's not uncommon to see different people making different choices about whether or not to include the dark energy piece as part of the stress-energy tensor.