There are too many points to answer here, but I just mention some major ones. It quotes Cerf and Darrigol that I have answered on this blog.

First of all: Poincaré did maintain the mechanist aether as crucial.Absolutely not. You will never see a quote to back this up, as Poincare always said that the aether "is only a convenient hypothesis ... will be thrown aside as useless." His theory did not depend on the aether.

The space and time transformations improved by Poincaré from Lorentz were therefore based on a set of "fictitious" transformations: since they had been obtained based on systematic errors during their measurements. Einstein's theories differed greatly.I don't know whom he is quoting, but Poincare was the first (in 1905) to say that the transformations form a symmetry group of space and time. That view was adopted by Minkowski in 1907, by most other physicists in 1908, and finally by Einstein in 1909.

The fact that Einstein's work on Special Relativity put the pieces together and revealed the complete theory in a coherent, correct and provable formulation is not really disputable.This is nonsense. Ever single principle was adopted by Lorentz and Poincare years ahead of Einstein. Einstein added nothing.

Lorentz and Poincare developed most of the math used, but never fully embraced the principles behind it.

You have been given the facts of how Einstein's and Poincaré's work are not interchangable, how they differed, how they did not accept each others work et al.Einstein told the story dozens of times about how he invented special relativity, but he was never able to explain how his theory was better than Poincare's. Einstein sometimes attempted to explain how his 1905 work was better than Lorentz's, but always gave arguments based on what Lorentz had done ten or more years earlier, and avoided Lorentz's recent work.

Poincare did explain how his theory differed from Lorentz's. After Einstein's 1905 paper appeared, it was called the "Lorentz-Einstein theory" as everyone agreed that Einstein's paper was just a recapitulation of Lorentz. Within a couple of years, it was universally recognized that Poincare's approach was superior.

Here is a timeline if the major concepts of special relativity.

^{2}(Poincare 1900)

Einstein's first relativity paper was in 1905. He had an exposition of most of the above concepts, but did not have the most crucial ones -- the 4-dimensional spacetime geometry and the electromagnetic covariance. He had no new ideas or formulas. He did not have the essence of the theory as it is known today, or even as it was known in 1908.

The attacks on Lorentz and Poincare are mostly based on allegations about their beliefs, and not what they said. This is especially true about the aether. Their theories did not depend on any properties of the aether, and they explicitly said so. While they occasionally later used the word, so did Einstein.

I don't know how anyone can understand relativity, read the above timeline, and still credit Einstein. If you read an article by someone defending Einstein, I suggest trying to figure out whether he agrees with the above timeline.

Update: LionAxe has it backwards about the aether. Lorentz wrote in 1895 that "It is not my intention to ... express assumptions about the nature of the aether. ... we cannot speak about an absolute rest of the aether". Einstein wrote in 1905 that "the view here to be developed will not require an 'absolutely stationary space' provided with special properties". Einstein always admitted that he based his 1905 paper on Lorentz's 1895, and they were saying essentially the same thing about the aether.

Poincare proved in 1905 that there was a symmetry group making all moving frames equivalent, and that there was therefore no privileged frame. Poincare never said that there was a privileged frame. If you think that he did, then show me the quote, and show me just what privilege that frame had in the theory.

LionAxe continues to complain about things that Poincare got completely correct, such as clocks in a moving frame showing the local time in that frame. That is an essential concept of special relativity due to Lorentz and Poincare, and it has been taught in the textbooks ever since. Einstein never had such an original and brilliant idea in his whole life. Lorentz got the Nobel Prize in 1902, and one of the arguments for it was his invention of local time.

Update: I asked LionAxe to show me where a mechanist aether was ever crucial to Poincare's work. He supplied "We know nothing as to what the aether is" (1904 lecture) "Does our aether actually exist? We know the origin of our belief in the aether." (1902 book) "Thus Lorentz's hypothesis is the only one consistent with the inability to demonstrate absolute motion" (1905 long paper) I have corrected the quotes using my sources.

In none of these does Poincare say that the aether exists, or that a privileged frame exists, or that the aether is needed for his theory. On the contrary, he repeatedly says that the aether is just a convention, that it will eventually be considered useless, and that a symmetry group makes all frames equivalent.

On the other hand, Einstein frequently says things like "It is essential to have time defined by means of stationary clocks in the stationary system". Einstein uses a privileged frame throughout his famous 1905 paper, and he is never able to show independence of that frame. Poincare proves independence using the symmetry group.

Update: I did not realize that Bjerknes had already refuted LionAxe.