Where are my desktop files actually stored? - My HD failed!

I have been running my iMac on Catalina, from an external SSD drive. Also using iCloud with plenty of storage.

A few days ago I got the white no entry sign, upon startup which meant the SSD had given up and I could not start up my iMac.

I tried first aid on the SSD and got this message (see attachment).

I was able to create a new user account, and get my iMac back up and running from the internal HD.

Now, my main problem is that many files which were on my desktop (supposedly in iCloud too), are no longer there.

When I restored all my files from iCloud I noticed that many were missing - and the files that were there were no longer in the folders - just hundreds of loose files on the desktop.

So now my main question is where are the lost files?

Would they be on my failed SSD drive?

Why didn't iCloud save/sync everything, instead just a seemingly random selection of files.

I am not sure if using iCloud means only the files are stored in iCloud - OR, are they also stored on the HD as well?

If they were stored on the external SSD drive, then I can look into taking it to a data recovery company to try and retrieve my precious files.

Thank you in advance for any help or advice anyone could give me.