According to the general theory of relativity, every observer will measure the same speed of light $c$ in vacuum, if they measure in their local inertial reference frame.
I assume that this statement is valid in the following cases:
When measuring within a different gravitational potential.
When the observer moves in the same direction as the light.
When the observer moves in the opposite direction from the direction of the light.
In addition to length contraction, is gravitational time dilation responsible for 1, while (dynamic) time dilation is responsible for 2 and 3?
If I'm not mistaken, length contraction and time dilation had to be added in order for the speed of light to stay the same and match c. Later, these phenomena were confirmed and are considered real. That's why I suppose that we can now say this: Gravitational time dilation is an effect that causes observers in their local inertial frame of reference to measure a constant speed c regardless of the strength of the gravitational field. Also, time dilation and length contraction act on the observer's measurements so that, regardless of their speed and direction, they measure the speed of light c, in their local reference frame.
Einstein's postulate is not the cause of the constancy of the speed of light, but the real (proven) phenomenon of time dilation is the cause of the constancy of the speed of light. Is that point of view correct? That is the essence of my question.
Thank you for taking the time to answer my question.