Converting non-gaussian dataset to gaussian dataset

Since anomaly detection works better with gaussian dataset, we’re advised to transform gaussian to non-gaussian dataset by some multiplication or log operations, but can we just do that without any consequences of error? as there is no step involved of undoing the transformation.

After the model is trained if you want to use it for anomaly detection you can always use the inverse of the transformation after you obtain the output of the model from the observed features. This output will exhibit the properties of whatever transformation you did so you need to apply the inverse of the transformation used. All the transformations shown had well defined inverses (almost everywhere). Moreover, the output of the model once transformed by the inverse will no longer be gaussian and should have a distribution close to the one of the original data.
So no I do not think there are consequences of error unless your model is not well specified to begin with.