About this MAC/Storage showing incorrect SYSTEM size
Solution 1:
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.
Solution 2:
Figured out the issue in my case.
Steps:
cd /
If you see a folder called 'cores',
type cd cores
If not, you can ignore the rest of this post.
type ls
If there's anything in here then it's probably the cause or a significant contributor to your issue..
type sudo chmod -R 777 ./
Enter your password
type rm -rf ./
And yeah this is relatively safe to do. The files are just core dumps (basically diagnostic logs that are generated when your computer crashes, as far as I know)
The storage tab in my TopLeftCorner->AboutThisMac instantly registered the 150GB that was just made available.