Restoring recovered files from a partition
No - the original state had files in specific locations and your recovery shows that that directory structure was lost.

So it sent "all the kings horses and all the kings men" to collect the parts of Humpty Dumpty but since the location of the parts is missing - it's not clear that even if you retrieved all the pieces - you would be able to get them in the correct places.

I would advise you restore all the files to a macOS formatted drive and set it aside. When you find you need to search for a specific file or text - you can use spotlight to search that drive for potential matches and copy them over to a place where you would like them to live. It's almost certain that the software you choose has instructions covering exactly how to do this operation in detail.

To summarize, data recovery isn't a substitute for a proper backup system. Those record durable and often redundant copies of file location data so you can always put things back where they belong as well as know if any one piece is missing since everything is cataloged "before the fall."