Cleaning up 113GB library with many duplicates in photo stream

There are many duplicate detectors around. If you need to find duplicates of edited versions and similar shots, try Photo Sweeper.

It can compare the photos based on histograms and bitmaps and is not only looking for duplicate files based on the file attributes. You can configure it how to resolve conflicts and which photos to keep in case of a duplication - the photo with the larger pixel size, the photo with key words assigned, the newer version or similar.

Also, are deleted photos also removed from a vault when the vault is updated?

Yes, if you update a vault, the duplicates will be removed.

PhotoSweeper is good, but I still have work to do.

You have to define, which photo you want to keep. At least you can do it in Photo weeper. The apps, that do not allow you to define your preferences, will probably delete the wrong versions. There is no way to do this automaticlly, that will be good for all use cases. I usualy want to keep the photo with the larger pixel size, and the version with the most recent edits, the version that has GPS assigned, etc.

The best strategy is to rely on the duplicate detection on import and never, ever to import duplicates in the first place.