disk used + available >> capacity

You are misunderstanding the meaning of "Available" which is a common mistake since it is a very misleading term....notice the Purgeable value in parentheses. You only have about 24GB of Free space left which is the absolute bare minimum needed to run macOS. See my explanation of Apple storage & terms in my post here:

Storage help. Trying to update but no room - Apple Community

Free = Available - Purgeable

25.36GB = 203.48GB - 178.12GB

It is very unfortunate Apple decided to use such a misleading item/term as "Available".....Apple should have focused on the more critical value of Free storage space.

If you have linked files into iCloud, the Master copies of those files are on iCloud, making the space they occupy on your Mac "purgeable" in case of emergency.

You can only continue this for a while. Eventually, you will need to buy a bigger external drive.

Only 30 GB remaining means your disk is essentially Full. For context, MacOS uses over 9 GB to go from cold start to fully operational.

Storage on recent versions of macOS and APFS volumes is complicated. I don't truly know everything that macOS is doing these days. In fact, there are areas even within your own home folder that you may not have complete access....especially in the hidden Library folder due to the new Privacy & Security settings macOS now employs. I recently used OmniDiskSweeper to look for the largest files & folders on my Mac. This app informed me that I would need to launch it with "root" privileges to see as much as possible, but even launching the app with "root" privileges, the app still mentions there are items it cannot access. I never had time to investigate exactly what those items may be. So you may not be getting the correct information even from the Finder.

FYI, I just did a quick check of my Mac using OmniDiskSweeper, and even with root privileges there are multiple items in my home user folder which are inaccessible. It seems those areas are for special Apple services.....probably cloud based services so they have enhanced privacy & security settings.

Plus, the macOS storage management information is known to be incorrect at times when it comes to assessing what is using storage for various categories.

All you can do is control what you store in the home user folder and configure your backups so that the backup APFS snapshots are not retained. I don't use Time Machine, so I don't know what options are available....I'm guessing not too many options, but I have heard some third party backup apps may have options on how long APFS snapshots are retained.

Here are various Apple articles regarding storage management on macOS:

Optimize storage space on your Mac - Apple Support

Change Storage settings on Mac - Apple Support

See used and available storage space on your Mac - Apple Support

Purgeable space can consist of all sorts of things. Unfortunately Apple does not list what specific items make up the Purgeable items at the moment since Purgeable space/items are controlled by macOS itself. iCloud is just one thing that could include items in Purgeable. APFS snapshots as mentioned in the post I linked previously is another possibility along with other things.