Please help me recover the deleted files on Mac. Unaware of the potential consequences, I erased every PDF and Word document that was typically located in “Recents” and “Bin.” Subsequently, I discovered that those records have also been permanently erased from elsewhere. Many thanks
The Recents folder in the sidebar of Finder windows is not a real physical disk folder. It’s a smart folder since it automatically searches Spotlight for the files you’ve used the most recently. All of the files that appear in the Recents folder are stored in several folders throughout your Mac.
When you delete the files from the Recents folder, it indeed deletes the files from the original locations and are moved to the Mac Trash, equal to the Windows Bin. If you have already emptied them from Mac Trash, you can only recover deleted files on Mac with backup or third-party data recovery software.
If you have deleted those PDF and work documents from the Recents folder and emptied the Mac Trash, they are permanently deleted from Mac. Have you backed up the Mac with Time Machine before the deletion? If you have enabled Time Machine before and connected the backup drive to the Mac before the action, it automatically backs up the Mac, you may try to restore them from the Time Machine backup.
No, there is no backup 
It seems that third-party data recovery software is my last resort. Any recommendations?
If so, you should perform the data recovery on your Mac ASAP before the deleted data is overwritten. You can free download iBoysoft Data Recovery for Macon your Mac, this tool enables you can scan the Mac drive, filter and preview the scanned results, and recover the desired items to a different location.