Is it not true, that due to the equivalence principle, the source for inertial forces is the same as for the gravitatipnal force: mass, or more general, energy cöncentrations?
No. The equivalence principle is assumed proportionality of 2 observations about bodies. One of the problems with Newtonian mechanics is that it was not derived from more basic (fundamental) postulates.
Hinnerk Albert In the Spacetime Wave theory, electrons protons and neutrons are considered to be looped waves in Spacetime. This explains how mass curves Spacetime and why mass responds to Spacetime curvature.
So General Relativity and the Spacetime Wave theory together fully explain the property “mass”. There is no need to hypothesise the existence of a Higgs field.
The idea of fundamental particles being looped waves in Spacetime also explains the property “inertia “. Spacetime presents zero resistance to moving looped waves in Spacetime but to accelerate requires an external force. Being looped waves in Spacetime means that they reside in the medium of space. Hence their inertia.
Conference Paper THE UNIFICATION OF PHYSICS (Conference Paper)
The gravitational inertial force in General Relativity consists of two terms: the term created by the divergence of the gravitational potential and the second term created by the derivative of the velocity of the space rotation by time.
Your question is excellent... This situation is well described in my next article.
Article A 2017. Fizikai Nobel-díj „gravitációs hullámai”
where it is a proven fact that the discovery of LIGO, on which it is based, was a fabrication. The public was greatly deceived by the scientific researchers and the Nobel Committee.