MacOS – Catalina Update Fail Purgeable Storage

Go in the Recovery menu (hold cmd+r), in the top left corner, you should see the Apple logo. Click on it and select the boot disk, which should appear as your internal hard disk, you will be prompted to enter your password to decrypt it and you should be good to boot into your old system.

I spent about a year working with Apple technical support on something that sounds just the same. The good news is that, assuming your problem is the same as mine, there is an easy fix. The challenge in diagnosis is that some interaction between iCloud and the Finder appears to be involved. iCloud's involvement is why problem persists across reinstalling the system, etc.

They fix was to delete either the dyld shared cache or the XPC cache. Unfortunately, I can't remember which it was and can't find my notes from then. But, since they are both just caches, there is no harm in deleting either or both.

The best way I found to do it is to download the Onyx app (free from https://www.titanium-software.fr/en/index.html). Under the "Maintenance" tab withing Onyx, you'll see the option to delete either or both of those caches. Do so, reboot and see if your problem is fixed. Once I did this, it fixed the problem entirely and it hasn't reappeared in over 2 years. There is probably a way to do this from the Terminal (indeed, Onyx is mostly just a wrapper over command line functionality), but Onyx worked great for me. I hope this helps you.