Startup drive (500 GB SSD) reports disk almost full; but backup of drive is only 147GB in size

One other thing: is it possible that you have another APFS volume in the same APFS container?

This would not show in the image above; but it would show in Disk Utility: below you see the normal two volumes, Macintosh HD and Macintosh HD - Data, plus a third volume. This third volume shares the available space in the container, but would not be cloned by CCC. This might explain the discrepancy.

You may try restarting in Safe Mode, then restart normally. This may clear some large caches.

Also: maybe some of it is from local Time Machine snapshots.

Tell us what is the output you get by typing the following in Terminal:

tmutil listlocalsnapshots /

Well, there you have it!!!!!

Your drive is littered with snapshots.

You can delete those snapshots, but I tend to prefer thinning them.

The form of the command is this:

sudo tmutil thinlocalsnapshots / 100000000000 4

Notes:

1) Since this requires sudo, you will be asked for your password. Type it (nothing will show as you type, not even bullets or asterkisks - that is normal), and press enter

2) The large number is the number of bytes you'd be trying to reclaim from the snapshots. You can use a larger or smaller number

3) The final number, 4, is the "urgency". 4 is the highest level.

OWC's article, Working With macOS Snapshots, is a very informative article about how snapshots are created, what they do and some of the problems that can occur.

Mike Bombich also wrote a detailed post about snapshots, Leveraging Snapshots on APFS Volumes. I mention this because your Terminal screenshot shows CCC creating snapshots for you on a daily basis. If you don't want CCC doing that, you can turn it off in CCC Preferences.

It's also curious that TM has created multiple snapshots on two successive days - 13 on July 7 and 8 on July 8. That doesn't look right to me and I suggest investigating why that's happening.

These snapshots should not accumulate... I don't know why they are doing that.

Sorry, I don't know how to prevent their creation.

And, yes, I think this totally related to the problem where Time Machine backup fails. Not sure exactly how, but it sure is.