photo libraries after upgrading to iCloud Photo Library

iCloud Photo Library is a syncing service. Any photo you delete from a device where iCloud Photo Library is turned on will also be deleted from iCloud and from any other device connected to that iCloud Photo Library. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: iCloud Photo Library - Apple Support

At this point, do we need to keep the large library files that are on our laptops? If the pictures are truly synced and stored in the cloud, I don't see the need to keep the original libraries that were stored locally for over a decade. Or is there some coding that would need those files kept on our laptops?

Keep the local Photos Library. If you do not keep the local Photos Libraries, you cannot use the Photos.app to access the library in iCloud. You will be reduced to using the web interface at www.icloud.com and the Phots.app on that web page. It will be very limiting to be reduced to the web interface. You cannot search for photos and you cannot edit photos there. It is only useful for emergencies, when you do not have access to your computer.

Keep your Photos Library on your Mac, so you can use the Photos.app there. The option "Optimize Storage", recommended by FoxFifth, can shrink the Photos Library to a tenth of its original size. But if you use it, you will always need an internet connection, if you want to edit photos or share them. Alternately, move the Photos Library library to a small, portable drive and plug the drive in, when you want to work with Photos. You can share the local photos library on an external drive between your laptops (Sharing photo libraries among multiple users - Apple Support).

Don't be surprised if the amount of free space on your Mac doesn't increase as much as you expect when you delete the library. Through a bit of somewhat confusing methodology, the space in Finder shows for both libraries but isn't actually what is happening. See the following:

Photos saves disk space by sharing images with your iPhoto or Aperture libraries - Apple Support

and

http://osxdaily.com/2016/05/20/delete-iphoto-library-mac/

If I remember from what I read when I migrated, it said not to delete the iPhoto library because they are not duplicated in the Photos library. But that's over 100 GB sitting on my laptop, yet stored in the cloud? If iCloud is truly just syncing, then wow, not a space saver at all and if I recall correctly, they promote iCloud Photo Library as a way to store large libraries and open up space on the devices.

Sorry that I misunderstood your question.

The iPhoto Library is not necessary to run Photos. Photos copied all photos from iPhoto to a new library and both libraries can be used without the other library. Keep a backup copy of your iPhoto Library on an external drive, just in case you should later discover that a photo did not correctly migrate to Photos.

Initially, right after the migration from iPhoto to Photos, the iPhoto Library and the Photos Library shared the storage for the photos and so it did not matter to keep two libraries, but this sharing is no longer possible, since you moved the photos to iCloud. So you can now delete the iPhoto library, if you have all photos you want to keep in your Photos Library.