Does estimating OIRFs from an SVAR (with uncorrelated errors) mean we are orthogonalizing the error structure twice? In a normal VAR, we can orthogolize the errors via Cholesky decomposition and estimate OIRFs. Thus, transforming the structure of the errors so that they do not correlate.
In an SVAR, asumming we impose an orthogonal structure on the errors directly so that they do not correlate. And so if we estimate OIRFs from an SVAR instead of just IRFs, are we not orthogolizing the error structure twice? First, through a direct imposition of an uncorrelated error structure by specifying some matrix. And second, through Cholesky decomposition if we estimate OIRFs.
Usually if you are estimating a SVAR model you would use structural impulse response functions (SIRF) not orthogonalized impulse response functions.  SIRF are not exactly the same as just IRF or OIRFs. SIRF already takes the identification problem into account when the SVAR is estimated.
To learn more about this you can have look at this blog about impulse response functions in R - the blog is brief but explains difference between simple impulse response, orthogonalized impulse response, structural impulse response and generalized impulse response. More info can be found in sources cited therein.