Same as Fig. 8, but including in gray (orange) the 95% C.L. on the fractional errors assuming that the EW distribution we used to interpret the mock observation is a Gaussian constructed from the same data (log-normal distribution from Tang et al. 2024a). In other words, the mock observations and forward models are generated using different EW distributions (see text for details). The fact that the C.L. demarcated in gray, orange and blue roughly overlap indicates that our results are not sensitive to our choice of the emergent EW distribution.