a little bit of skewness works fine. Idea data are normalized, not in the real world. All you can do is check if you have any outliers by performing a quartile test or finding the z score. Choose a range of z scores and see what you can achieve. Additionally, model performance can depend not only on one feature but others too so make sure to check for the distribution of other datasets. Once you have an idea of the data distribution of entire features you can then decide if you want to scale or normalize your data.

A little bit of skewness is ok. In real world, the data is not always normally distributed. All you can do is check if you have any outliers by performing a quartile test or finding the z score. Choose a range of z scores and see what you can achieve. Additionally, model performance can depend not only on one feature but others too, so make sure to check for the distribution of other features from the dataset. Once you have an idea of the data distribution of entire features, you can then decide if you want to standardize or normalize your data.