Bruce Popp (2020)  argues that Poincaré ([Poi05] and [Poi06]) developed a correct relativistic theory of electrodynamics that achieved both substantial and incomplete progress to a theory of special relativity by a different route from Einstein. This route had its origins in work on radioactivity and electrons. His 1905 and 1906 papers are immediately based on his close reading of [Lor04] and the three divergences from Lorentz that Poincaré identified. For example, he understood Lorentz’s presentation of the transformations based on corresponding states was flawed. Poincaré provided the correct form for the transformations and the understanding that they were coordinate transformations. It is this corrected form that Poincaré named “Lorentz transformations” and that match the form and understanding given to them by Einstein [Ein05c]. Poincaré shows that thus corrected the transformations are a group corresponding to a rotation in four-dimensional space with three spatial and one time dimension and that the space-time interval is an invariant of this group.
Popp emphasizes that while, as this summary suggests, Poincaré would have been justified in making a series of strong statements about his findings, very surprisingly he did not. In fact, Poincaré does not seem to have understood and synthesized what he showed in 1905. Worse, he contradicts himself in later writing adding to confusion about his work and positions, notably concerning the ether. Popp indicates that this is one reason why Poincaré’s alternate path to special relativity is not fully realized. Another is that Poincaré shows no appreciation of the implications for simultaneity and time; in brief there is nothing comparable to Einstein’s discussion of moving watch hands and trains arriving.This is all conventional wisdom, and here are his main arguments.
References Popp, Bruce D. (2020). Henri Poincaré: Electrons to special relativity: Translation of selected papers and discussion. Cham: Springer International Publishing. ISBN 978-3-030-48038-7.
Poincare did not brag about his work, as Einstein did. Poincare obviously thought that his papers speak for themselves. He didn't brag about his many other original works either. That was common for scientists. Einstein was the exception, as he made great effort to claim credit for the work of others.
If Poincare understood what he wrote, then he was years ahead of Einstein. The Einstein fans say that this proves that Poincare did not understand what he wrote, but of course that never happens. Obviously Poincare understood what he wrote.
Poincare did not emphasize simultaneity in 1905. As you can read in the Wikipedia article on the subject, Poincare discovered relativistic time synchronization in 1898, and regarded it as a solved problem.
Poincare's contribution has been forgotten. There is some truth to this, as Poincare's work is mostly remembered in two papers by Minkowski, who died shortly afterwards, and in all subsequent work that considers relativity a 4-dimensional theory.
It is amazing how scholars concoct these stories to credit Einstein over Poincare. Our current understanding of relativity is based much more on the work of Poincare than Einstein.
Poincare's works get mentioned on Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries | Lex Fridman Podcast #190. He is praised for his work on celestial mechanics, stability of dynamics, and topology. Discovering relativity is not even mentioned. Einstein's greatest accomplishment was just a poor plagiarization of one of Poincare's minor papers.
[Einstein is] universally acknowledged to be one of the two greatest physicists of all time, the other being Isaac Newton.Someone pointed out that polls by PhysicsWorld and UK BBC showed physicists saying that Einstein was the greatest, with Newton in second place.
There continues to be crazy over-the-top idolization of Einstein. Normally a book about a great scholar will simply describe what he did, without gratuitous insults about him being inferior to some other great man.
That's what the above book does. It recognizes what Poincare did, and then makes nonsensical disparaging remarks in order to say that Einstein was better. Maybe someday I will see an Einstein scholar write something like this:
Einstein's 1905 relativity paper was a nice exposition of Lorentz's theory. But it lacked references to earlier theoretical work by Lorentz, FitzGerald, Poincare, and others, and to crucial experimental work by Michelson-Morley and others. It failed to explain how his theory was any different from Lorentz's. Nobody saw any difference, and called it the Lorentz-Einstein theory. Einstein failed to grasp the spacetime geometry, the Lorentz group, the covariance of Maxwell's equations, or the implications for gravity. Einstein shows no appreciation of relativity as a 4-dimensional theory; in brief there is nothing comparable to Poincare's 1905 work, and nothing that led to further work.Whittaker did say something similar in his 1954 book. Einstein was sill alive, and could not refute it, even though his friend Max Born tried. So all serious scholars know that this Einstein credit for relativity is a hoax. The Einstein worship has only accelerated since then.