Vincent,
Should we have a threadlocal based implementation on OGRCoordinateTransformation object ?

Yes, one OGRCoordinateTransformation object per thread. See https://gdal.org/en/stable/user/multithreading.html : "Unless otherwise stated, no GDAL public C functions and C++ methods should be assumed to be thread-safe. That is you should not call simultaneously GDAL functions from multiple threads on the same data instance"

Even

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