coupling to matter

Mmmh, if both the Schwarzschild-solution as well as the gravitational waves are vacuum solutions and therefore only need the Bianchi-identity, would that imply that cosmology is the only way in which the field equation is actually tested?

The Schwarzschild-solution and gravitational waves solve the vacuum field equation \(R_{\mu\nu} = 0\), and FLRW-solutions are valid for a homogeneous and isotropic \(T_{\mu\nu}\) on the right hand side, so only there is coupling to matter involved - but of course it depends on what “tested” actually means: The field equation makes the job of propagating the curvature of spacetime (the Weyl-part) and of coupling curvature to the sources (the Ricci-part), and both are indispensable for a gravitational theory.