Can we think of space as any kind of aether in any way? I am not asking about the Michelson-Morley experiment in any way. I am specifically asking, if space (including the fields that QFT describes) itself can be thought of as any kind of aether  that propagates energy (in the form of waves) somehow. I am asking in what way this famous quote could be interpreted as space itself having the characteristics of an aether.
I have read this:

according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.

And this one:

Specifically, the notion of medium that one can in principle detect one's motion relative to is what has been ruled out by experiment. So, although one must be careful with the word aether to exclude anything that violates Galileo's principle and yields Lorentz-invariant predictions as being in conflict with experiment, I personally kind of like the word as a metaphor for empty space to emphasize the 20th century achievements of general relativity and quantum field theory. We can describe how empty space takes different geometry through the Einstein field equations. The quest for quantum gravity can be thought of as seeking to understand the mechanisms and that machinery of empty space that lead to the EFE description: quantum gravity can be thought of as the quest to find out how the Lorentz-invariant "aether" works.

Isn't the aether existent?
The last answer says, that today we know that space itself if not some kind of medium that we can detect motion relative to. But today we know that space itself (and the fields it includes) is somehow able to propagate energy in the form of waves of all kinds (EM, gravitational, gluons). Space itself can stretch, squeeze, expand (and probably contract inside a black hole), curve. Thus, can we say that in any way space itself acts as an aether, we just cannot detect any motion relative to it? So basically, there is no aether in space, no medium (in the vacuum of space), but can we say that space itself acts in any way as some kind of aether?
Question:

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*Can we think of space as any kind of aether in any way?

 A: What did the Michelson Morley experiment exclude?

The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles. This result is generally considered to be the first strong evidence against the then-prevalent
aether theory,

This experiment cannot exclude an ether that respects Lorentz invariance . Thus , as far as I understand, the quantum field theory fields that cover all spacetime and are Lorentz invariant could be a model of a "medium" since interactions propagate on these fields. The same would be true for models that propose a  Lorenz invariant substrate on which interactions happen . Those "aethers" are not excluded by the experiment.
A: It sounds to me that you are asking about the theory of Loop Quantum Gravity.  This is the theory that space itself is particulate, made up of extremely small particles or loops.  This theory is based on relativity, but it does not imply an aether.  Rather, space is described as the stage on which other things occur, like the waves that you are describing.  I'll note that LQG is considered as an alternative to string theory.
Physicist Carlo Rovelli, (in his book Covariant Loop Quantum Gravity) described them shaped as tetrahedra (a 3 dimensional triangle), noted, “The physics of quantum gravity is the physics of the quantum fields that build up spacetime… A region of space can be described by a set of interconnected grains of space… The length of these links is determined by the field itself, because geometry is determined by
gravity.”
Dr. Don Lincoln from Fermilab said “When you add mass and energy, you can distort the shape of the little volumes of quantum space… Bending space and time has a property that you can distort the local definition of space.” So this would mean that an energy wave traveling through space would in fact be a wave of changing shapes of these loops.
And in my own speculative theory, I would say that it is this addition of energy distorting the shape of the little volumes that becomes a clear definition of the warping of spacetime that is the basis of gravitational theory.
A: Whether space can be thought of as a substance, in any way, is an interesting question.
When the Michelson Morley experiment ruled out motion of the earth relative to the aether, there were scientists who wanted to keep it as a concept and wondered if the aether moved with moving objects aether drag hypothesis
...but there were various problems with that idea.
So the aether went out of fashion, although there are some modern aether theories.
As you say there are various 'properties of space' electromagnetic fields etc. and scientists talk of the 'expansion of space'.
So perhaps there is role for the aether as an aid to our imagination, although most scientists would use Occam's razor and claim that until there is definite experimental evidence for it's existence, then we should presume it doesn't exist.
