About this MAC/Storage showing incorrect SYSTEM size
It seems illogical but it is really not. The important distinction to note is that the screenshot does not say "192.29 GB free", rather it says "192.29 GB available".

This is because the system part (shown as 159.77 GB) includes disk caches. Most of these disk caches are purgeable, meaning that they can be automatically freed up when space is needed.

So you have 191.29 GB available for you to use when you want - but while you're not using them, the system is using them to speed up operations using caching.