As for whether Tesla can foresee several major effects of general relativity, it is unlikely. First of all, experimental physicists give their conclusions based on experiments, and classical gravity theory combined with special relativity can also explain the gravitational redshift and light bending of general relativity, so I personally think that even if Tesla finds these effects in his experiments, he may use classical gravity theory to explain them-then that is to say, the experimental conclusions and theoretical predictions are wrong.
With poincare, it is unlikely. First of all, Poincare is good at mathematics, but his physical foundation is too poor-special relativity is just around the corner, but he has failed to establish a new physical system. Secondly, general relativity needs more advanced physical ideas to explain than special relativity. Even if Lao Pang established the general theory of relativity, I believe he is similar to Hilbert. Hilbert established the gravitational field equation with the world function, but he didn't know where this thing should be placed in the physical system. After a lapse of nearly half a year, Einstein published a paper-the completion of general relativity. It can be said that if Einstein does not establish the general theory of relativity, no one will be able to establish it within 50 years (that is, in the first half of the 20th century).
Einstein's famous saying: I don't put forward the special theory of relativity, but someone will put forward it in five years; I don't put forward the general theory of relativity, and no one can put forward it in 50 years.