Copy files from Finder search results with directory structure/hierarchies intact on macOS?

I found results for similar variations of this question, but none that really provided a solution for my specific case.

I have a lot of preset files with a specific extension (.tfx) on a backup drive. The files are scattered around in different folder paths within a specific backup folder structure. I need to find a way to copy all of these files with their directory structure intact, and I need to be able to filter the searched results by date range, and only keep the most recently modified versions of any file.

e.g.

Source:
BackupDrive/Backup_20201201/folder1/subfolder1/subfolderA/file1.tfx
BackupDrive/Backup_20191101/folder1/subfolder1/subfolderA/file1.tfx
BackupDrive/Backup_20201001/folder2/subfolder2/subfolderA/file2.tfx
BackupDrive/Backup_20200901/folder3/subfolder3/subfolderC/file3.tfx

Destination:
Documents/FromBackup/folder1/subfolder1/subfolderA/file1.tfx
Documents/FromBackup/folder1/subfolder2/subfolderA/file2.tfx
Documents/FromBackup/folder2/subfolder3/subfolderC/file3.tfx

The catch here is the ability to find and copy only the specific file type, and only modified within a specific date range, and so that older versions of the same file in the same relative path would be overwritten by the newest versions without prompting me to confirm every case where this occurs (because there will be hundreds of them).

I also need to eliminate the dated backup folders from the target hierarchy so that there is only one hierarchy in the target path instead of several copies from backups I made on different dates.

The ideal solution would be to make an app using Automator so that I could simply use Finder to find the files I want to copy within a specific backup path and modified date range, then drag/drop all of those results onto the app, which would then prompt me for the parent/destination folder for the files I want to copy with their folder hierarchies intact. And if any of the files being copied exist in the target location and have a more recent modification date, the newer files would not be overwritten.

I figured out how to do this on Windows 10 using a batch script and robocopy to basically sync changes from one folder path to another on a mounted network drive. But I’m not sure how I can do this on macOS.

Thank you in advance for anyone who can help with this!