"If true, this means that everything that Einstein sold is a complete lie."

That's not factually correct. More information is necessary before that can be said for sure. There are various mechanisms that have been conceived to appear to get stuff to move faster than the speed of light. The speed of light has also been challenged as constant. There are all sorts of very significant aspects of the special and general relativity equations that are constantly being questioned and challenged in physics. It's possible that discovering one or another of them could challenge the entire theory, but more likely that the theory would adapt to such by being modified.

Newtonian physics, a cosmological whole, did get thrown out when Einsteinian relativity came in. Newton's orbital calculations, however, didn't. SpaceX and NASA probably use them every time they shoot a rocket at something, because they're close enough for rocket science and much easier and simpler.

E=MC^2 is deceptively simple.

However, in the centuries between Newton and Einstein, a great deal of very complex thinking went into physics, and Einstein's relativities didn't just arise out of the blue, but out of that ferment and mathematical basis. When you dip your toes into that body of work you find that adding this or that didn't throw the whole out. Quantum physics completely counters classical physics, and Einsteinian relativity is classical physics. There has been great tension between the two aspects of physics since Einstein stated his above formula, and continues today.

Those Quantum physical equations didn't throw Einstein out, and Einstein didn't throw Newton out (at least not his calculations). Science usually accepts new understandings by adapting, and even apparently contradictory facts are held in tension available to the next Liebniz or Gibbon to resolve.

Tesla's work advanced, but didn't break physics, at least not to my layman's understanding. The forces at play in spacetime are what Tesla dealt with, and not the spacetime itself. Your OP indicates there is some discontinuity between these physical mechanisms, and doesn't cite a formula or mechanism from Tesla, or even any single thing either Tesla or Einstein said that indicates either of them challenged the others theses.

They were contemporaries, you know.

Edit: I am still watching Sheldrake's video. The various assumptions of academia about consciousness he mentions are being challenged. I myself recently discussed my theory of quantum consciousness that proposes reasons why esp and paranormal experiences may have factual basis. This doesn't 'break science'. In the same way the big bang theory didn't break physics when physics reckoned the universe had always existed.

Science is a method. Hypotheses need to be tested experimentally to ascertain if they are factually correct. Despite great support from Penrose and others, I haven't proved anything by positing a hypothesis, and even if the theory is proved, it won't unprove anything else. Assumptions aren't science. Nothing benefits science more than the breaking of it's hidebound assumptions, and you can find them in every field in which researchers have devised theories and commandeered academic posts and grant monies.

Gatekeeping isn't science. Interpretations of experiments matter. There are people whose careers depended on interpretations of experiment that have been disproved, and this has caused great disruption of the lives of researchers that disprove the interpretations of gatekeepers that command funding during their dotage. I suggest that is what is at risk, not science, nor the laws of physics.