How do I merge two large Photos libraries without losing photos?

As Yer_Man says, the very best way to deal with multiple Libraries is with the trusted 3rd party app PowerPhotos ($35.) It's good for all sorts of things but, as you see, it costs. Thankfully, it's not one of those things that has the dreaded "in app purchases." You get lots of options with merging libraries. There is a free version, but unfortunately, it doesn't do merges. There is good documentation at their site, and you can look at that before you buy.

You can also just use File>Import to import pictures from one Library into another. Photos will test for duplicates as it always does when importing. Unlike PowerPhotos, though, this method does not preserve albums and folders. In any case, merging large libraries can take quite a bit of time, and lots of duplicates will make the merge take even longer. You might win by deleting in one Library a bunch of pictures that you know aren't in the other.

By all means, be sure you have duplicates of your Libraries-- merging changes libraries, so it carries some risk.

The best and most efficient way to merge libraries is with a 3rd party app called PowerPhotos

https://www.fatcatsoftware.com/powerphotos/

When it merges it protects against duplicates as it works.

This app is recommended daily on here.