I've been experiencing the same AirDrop problem since upgrading to Ventura two months ago. I often would AirDrop all types of files (not just PDFs) from my iPhone or iPad to my iMac's Downloads folder in the past, but now my iMac doesn't receive them. I do hear the "ping" sound that indicates a file has been AirDropped, and the Finder becomes the active app, but my Downloads folder is empty. A search for the file name that was AirDropped turns up nothing, so I assume the file was never transferred. Strangely, I have no problem sending files from my iMac to my other devices via AirDrop. Are you able to send files from your iMac with AirDrop, or is that also not working?
My Documents and Downloads folders have not moved since upgrading. They're still in the Finder window inside my User folder, and they're still in my Dock, too. But I don't use iCloud to back up those folders; I use Dropbox instead. Have yours disappeared from both the Dock and your User folder? Hopefully you were able to locate your folders in your iCloud Drive, then simply copy the missing folders/files back to your local drive.