Lost files in cloud folder after system update

I saved my documents (many many files from work) to my local Cloud Drive folder because I wanted them to be save before I do the software update on my MacBook Pro. So I moved my files from the Documents folder to the local Cloud Drive folder. I did not check in my Browser if everything was uploaded correctly. And unfortunately the synchronisation didn't work/was turned off/whatever.

After I did the system update to iOS Sonoma, the local Cloud Drive folder was empty. Everything else, all files in my other local folders like Documents, were still there.

When I tried to open one of the files which were included in that folder, it said the original file was deleted. I searched my entire Mac, library, logs, trash, etc. - nothing to be found anywhere.

I also checked the Cloud Drive, it's trash etc., but it's not in the Cloud Drive as it was never uploaded as intended.

Question: Since the files were stored locally in my Documents folder before I moved them to the local Cloud Drive folder, can they be recovered? I don't have a timemachine backup.

Has anyone experiences with online recovery software (like wondershare etc.)? Could that help in my case? And finally, what is the best software to recover lost files?