For SEM, the normality assumption is not strictly required, but it is still useful to assess the distribution of your data to identify any outliers or extreme values that may impact your results. If the data is not normal, you may consider transforming the data to make it more normal, or using non-parametric methods such as bootstrapping or permutation tests to estimate the SEM parameters.

In OLS linear regression, normality is only required for the residuals (error terms) of the regression model, not the predictor(s) or dependent variable. So you only need to be concerned about the distribution of your residuals (error scores).

In structural equation modeling (SEM), the default estimator in many software programs is maximum likelihood (ML). ML estimation is based on the assumption of multivariate normality. If your data are non-normal, you can use robust ML estimation (e.g., Satorra-Bentler correction; Bollen-Stine bootstrap) to obtain robust standard errors and test statistics or you can use an estimation method that does not require normality (e.g., weighted least squares or WLS estimation). However, WLS requires very large samples to provide valid results, so people typically use the first option (robust ML estimation).

Many thanks for your helpful advice, Dr. Christian Gesier and Dr. Dinesh Kumar.