Robocopy move old files instead of override

Solution 1:

You can try these -

1. freefilesync

FreeFileSync is a folder comparison and synchronization software that creates and manages backup copies of all your important files. Instead of copying every file every time, FreeFileSync determines the differences between a source and a target folder and transfers only the minimum amount of data needed.

2. Windows File History

3. You can try creating a script Hints/similar questions -

3a. way-to-keep-a-backup-of-only-the-modified-files-in-a-directory

3b

how-to-backup-files-before-overwriting-them-with-rsync

--backup option of rsync

-b, --backup
With this option, preexisting destination files are renamed as
each file is transferred or deleted. You can control where the
backup file goes and what (if any) suffix gets appended using
the --backup-dir and --suffix options

3c. backing-up-specific-files-before-replacing-them-based-on-source-folder-contents

3d. use-rsync-for-backup-without-overwrite

Solution 2:

Syncthing and GsRichcopy360 are so far so good ,both have great features and solid for me so far in testing and using. Installation was painless, and uses WAY less resources than CPU. Both can do the required tasks in your question