I am now updated all the way to 13.3 and have experienced the same "File cannot be found" message since my initial upgrade to Ventura.
At first I was thinking it was related to Dropbox, which I use with the client-side app which integrates directly into Finder. I also use the Dropbox Backup tool to backup my Documents, Downloads, user home folder and Desktop. But I dispelled that after reading the initial post on this thread.
I use Preview pretty much all day long for reading and managing PDFs. I wondered if it was a bug with Finder and Preview, thinking maybe there was something in the Preview meta-data or potentially some other issue at the ACL level.
However, now seeing that this thread has so many similar yet unrelated complaints it has become clear to me that this is a Finder issue. The first suggestion to reboot into Safe Mode was a good one, but the more I thought about it the more it made me realize that there is nothing different about the way that I am operating on my system going all the way back to High Sierra. I am using Dropbox, Preview, and basic productivity apps.
I also thought about whether it was an issue with folder nesting, because I manage a massive archive of team files and they are deeply nested based upon workflows. But the problem persists between 4-5 level deep nested folders and my desktop.
The only factor I have not closed the book on yet is that I am now working on a MacBook Pro with an M2 chip, my first Apple Silicon system. I have never experienced the issue of "File cannot be found" on any of my Intel Macs. However, that gets muddied quickly because this is the only Mac I have owned that supported MacOS 13. So I leave open that there is a slim chance it's related to the M2, but have no way to verify or deny.
So I go back to the one commonality in all of these posts on this thread, it's something in Ventura that is the issue.