Einstein's return to aether So it seems like that Einstein returned to the concept of aether, but from the point of view of a general relativistic framework.
https://mathshistory.st-andrews.ac.uk/Extras/Einstein_ether/
This is often overlooked by modern theoretical physicists. Does the introduction of this aether from a general relativistic viewpoint have anything to say about the null result of the Michaelson-Morley experiment? If such an aether is hypothesized to exist, would it not cause a non-null result for the Michaelson-Morley experiment?
 A: What Einstein proposed is to reuse the word, not to reuse the historical concept.
Let me make a comparison.
Caloric theory was a theory of what heat is. For a material to become hot it was supposed that a massless substance was diffusing into that material. This massless carrier of heat was called Caloric.
Later the concept of caloric was abandoned. Now, by that time the scientists had become accustomed to defining 'heat' in terms of presence of Caloric. If the scientist of the time would retain the definition of heat in terms of Caloric then they would have to avoid the word 'heat'. If heat = Caloric, and Caloric does not exist, then you can't use the word 'heat'.
Of course, what had prompted the scientists to abandon Caloric theory was that a new way of conceptualizing 'heat' had been developed: statistical mechanics: thinking of heat in terms of motion of the atoms/molecules that make up matter. The concept of 'heat' had been redefined.

In that 1920 talk, Ether and the theory of relativity Einstein points out that Lorentz had already stripped the concept of Ether of almost all physical properties.
Quote:

As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, that immobility is the only mechanical property of which it has not been deprived by H A Lorentz.

Subsequently Einstein points out that relativistic physics goes a fundamental step further:

We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.

In terms of relativistic physics: whatever experimental setup you are using: there is no such thing as attributing a velocity vector of the experimental setup with respect to the relativistic Ether.

As we know, the physics community of the time didn't follow Einstein's suggestion to reuse the word 'Ether'.
Sometimes a new word is adopted, or constructed, sometimes an old word is reused, in a completely new meaning.
Example of reuse:
There are theories of physics that involve the existence of something that is referred to as 'quintessence'.
The fact that the word 'quintessence' is reused does not carry any meaning. It's just a way of expressing that the description of this Quintessence requires a high level of abstraction.



[Later addition]
The underlying point is that relativistic physics attributes physical properties to spacetime. John Wheeler expressed that as follows. "Matter/Energy is telling spacetime how to curve, curved spacetime is telling matter/energy how to move." (Or words to that effect; there are a lot of paraphrasings in circulation) In terms of relativistic physics spacetime is a participant in the physics taking place; spacetime acts upon and is being acted upon.
Conversely, asserting that spacetime cannot have physical properties would deprive one of the means to formulate GR.

Maxwell's luminiferous aether is an entity that is always present, everywhere, existing in a neutral state. In that neutral state Maxwell's aether does not affect motion of material objects.
Maxwell's aether has internal degrees of freedom, and these internal degrees of freedom are such that Maxwell's aether supports propagation of electromagnetic waves.
As we know, electromagnetic waves affect motion of matter, which we take advantage of in radio receivers, and of course in our microwave ovens.
As we know, Maxwell's aether and Lorentz' aether have been abandoned, but of course we still need a way to account for the propagation of electromagnetic waves.
(Comparison: the phenomenon of heat is something that must be accounted for. You cannot not have a theory of heat. Caloric theory was abandoned because a better way of accounting for heat had been developed: the kinetic theory of heat.)
In terms of quantum theory there is an entity that is present everywhere, and photons are described as excitations of that omnipresent entity.
In quantum theory the expression 'electromagnetic field' is a reused expression. In terms of quantum theory the meaning of 'electromagnetic field' is fundamentally different than in classical mechanics. Rather than coming up with a new expression the existing expression was reused, in a fundamentally different meaning.

In terms of relativistic physics:
In the absence of a source of gravitational interaction spacetime is in a neutral state, and in that neutral state the direction of motion of material objects is not affected. The presence of a source of gravitational interaction sets up a bias in the state of spacetime, and that biased state acts as the mediator of gravitational interaction.
As to propagation of gravitational waves:
Back in 1920 it was very much unclear whether or not GR was a field theory that allowed/implied propagation of gravitational waves.
In order to support propagation of waves a medium must provide the following properties:
-it must support a biased state (a state away from neutral state)
-the medium by itself tends to return to the neutral state
-when the state is changing at a particular rate it tends to keep changing at that rate
Comparison to harmonic oscillation:
An elastic string under tension will support vibration because:
-there is an elastic force that tends to return the string to the least stretched configuration
-the string has inertia, so that when it has a velocity it will overshoot
As we know: it has been confirmed beyond reasonable doubt that GR spacetime supports propagation of gravitational waves.
A: Acceleration (observed from rotation) against totality of the masses of the world: To deny the ether means in the end to assume that empty space has no physical properties at all.. But the mechanical behavior of a physical system .. depends .. also on its state of rotation (Einstein means the acceleration we experience when we are in rotation (centrifugal force), which physically cannot be regarded as a characteristic of the system per se.
Mach tried to avoid the necessity of assuming something unobservable real by putting into mechanics an average acceleration against the totality of the masses of the world..
Einsteins argumentation for an ether for mediated action on distance: But an inertial resistance against relative acceleration of distant masses presupposes unmediated action at a distance. Since the modern physicist does not believe to be allowed to assume such an effect, he ends up with the ether again, which has to mediate the inertial effects.
Ether in the General Theory of Relativity: Mach's thought finds its full development in the ether of the General Theory of Relativity. According to this theory, the metric properties of the space-time continuum in the environment of the individual space-time points are different and co-conditioned by the matter existing outside of the considered area.

Does the introduction of this aether … have anything to say about the null result of the Michaelson-Morley experiment?

Neither Einstein nor the following scientists have made statements whether the aether is immobile between the moving celestial bodies or whether the aether near masses moves along with them.  For an aether locally moving along with the earth, the Michaelson-Morley experiment cannot recognize a preferred direction.
If such an aether is hypothesized to exist, it cause a null result for the Michaelson-Morley experiment.
