Except ... people have been arguing about "are all type Ia supernovæ the same?" since the 1980s, to my personal knowledge, and probably longer. So there has always been a weighting factor included in the calculation of the results which should reduce the effect of actually demonstrating that this, that, and those SN Ia are SN Ia2 while those are SN Ia1.
I'd expect the error bars to increase, moderately.
This doesn't affect the other steps in the "cosmic distance ladder". The red shift calibration against Cepheid variables (remember the 1940s discovery that there are two types of Cepheid, with different period : absolute luminosity relations, and how that completely didn't upend the rest of cosmology?) remains valid. Maybe a bit noisier if the SN1a[1 or 2] records need some sorting out, and possibly re-observation. It's not as if SN aren't already observed for years after their explosion until their light curves are lost against their host galaxy.
There were already hints that the infamous "Hubble Tension", between the CMB derived values for H_0 and the near-universe derived values for H_0 could be due to a systematic error in the "cosmic distance ladder", and this could be just the thing needed to remove the ~10% offset between the two types of estimate and bring them into alignment.