Transferring large photo library to new Mac with less storage

I, and many others, have a Library that has only my Favorites on it, so it's much smaller than the more archival Libraries that I have.

I am thinking that your are not using iCloud to synchronize your Photos Libraries-- is that correct?

First: are the two Macs using the same OS? A Library can't be used on Macs with two different OSs. Once a Library is upgraded to work with a newer OS, it can never be used on a Mac with an older OS. So, work on the older system, and then copy the new Library to the newer system.

By the way, you mention an external drive. How is it formatted? To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. Additionally, the drive can not have had Time Machine on it since it was formatted. There have been so many problems with using incompatible drive formats that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:

Move your Photos library to save space on your Mac - Apple Support

You can go two ways-- you can create, on a properly formatted external drive, a new Library, and copy your favorites into it. Or, what I did originally, was duplicate my Library, and then remove the pictures that I didn't want, leaving only Favorites. I went through each album in turn, and deleted pictures. This Library was a copy, so mistakes can be fixed.

Dealing the multiple Library is made much easier with the trusted 3rd Party app, PowerPhotos ($30). This allows whole albums to be copied from one Library to another, for instance, and it does lots of more helpful things.

When you move the small favorites library to the new Mac, you will need to designate it as the System Library.

If your systems aren't compatible with this, or if you're using iCloud, things may be a bit different. Let us know...

Buy yourself a 2TB SSD and back all you photos up to that and save the space on the Mac for other things.

I, too, have had hard drives go to the big upload in the sky. (By the way, CDs and DVDs don't last nearly as long as they said.) I now have more drives than I can count. Since I use a laptop, I've bought small, light, fast SSDs (at about $70/TB, now,) and I carry two with me-- one for TimeMachine backup and one that I copy important files to. Also, when I get home and plug in, I am connected to TimeMachine on an older mechanical drive.

My biggest problem now is keeping track of all the backups.