It is true that Lorentz transformations constitute a satanic minefield, but H. Lorentz and A. Einstein survived their navigation.
I-The modern proof of Lorentz transformations fabricated later makes us laugh
quite simply because there is no physical or mathematical proof.
Besides Wikipedia's errors, stating that "Lorentz derived the transformation from the special theory of relativity, as well as from the Lorentz force."
Noble Prize giant scientist H. Lorentz, while working extensively on accelerated electrons in EM fields, experimentally observed and introduced the Lorentz transformation equations as EMPERICAL equations.
Probably because he knew there was no proof.
In other words, Lorentz himself considered these transformations as a dependent or independent law of nature and never attempted to prove them.
Likewise, the modern proof of mass-energy equivalence E=mc^2 is ridiculed simply because this formula has no physical or mathematical proof.
The mass energy equivalence E=mc^2 is a universal law of nature.
II- On the other hand What happened later was that the giant A. Einstein succeeded in 1905 in proving this formula via his thought experiment on his sphere of light propagating in two inertial frames of reference.
In fact, Einstein's derivation is based on the constancy of the speed of light c.
which means that Einstein added nothing because the Lorentz transformations imply the constancy of the speed of light and vice versa.
What else !
Einstein then derived the mass energy equivalence formula E=mc^2 via another thought experiment by merging Lorentz transformations with Newton's law of motion in its general form F=d/dt)mv.
Again, Einstein didn't add anything here because the mass energy equivalence formula E=mc^2 implies Newton's second law of motion and vice versa.
1-A rigorous reformulation of Einstein's derivation of the theory of special relativity, IJISRT journal, February 2022.