None of these have anything to do with what I said. SR works just as well as classical mechanics with acceleration. If SR didn't work with acceleration, it would have never been accepted as a valid theory at all, it would have been a laughing stock, as acceleration was well understood since the times of Newton.

What general relativity does different from special relativity is that it extends the concept of relativity from inertial frames of reference to all frames of reference, even accelerating ones. In the process, it also explains the reason why inertial mass and gravitational mass happen to be the same, by tying the gravitational interaction fundamentally to the concept of acceleration.