I think Russ's idea of transferring to the new mac and organising there is a good one.
Some other things to think about. Do you really need to sort them out. If you get rid of all the folders/albums, photos can still display the photos by year/month/day in the all photos view. For my older images, I don't have any more organisation than that. Bear in mind also that photos has a lot of automation to help you find images - such as face recognition, automatic folders for panoramas, selfies etc.
Something else you can use is the smart albums. I too have a lot of old scanned photos. I've used a smart album to help me identify them. I've used the search "Camera model is empty" - because scans have not been taken with a camera, there is no camera model. It does also find screen shots, so it is only a starting point, but narrows things down a lot. There are many other ways you can use smart albums to search for particular images.
Also worth considering using keywords in your images rather than organising with folders and albums. Why?
Well lets say I tag all my old family scans with the keyword OldFamilyScan - I can then find them using the keyword rather than an album. OK - not much different than using album called "OldFamilyScan"
The power really comes though when you use multiple keywords. So lets say I add the keyword NT for all photos taken at a national trust property. But also add they keyword of the place - say BiddulphGrange or DunhamMassey or TattonPark
So at some time in the future, I can search for all photos taken at a national trust place - or those taken at just some of the properties, or just one.Now lets say I tag photos taken on holiday with the word Holiday. Now if at some point in the future I say "now what was that NT place we went to on holiday last year" I can set up a smart album looking for NT, Holiday and Date last year.
They can also be combined with face recognition - so I want to find photos at Biddulph Grange with Dad in them - can do it.