Transfer Photos Library to new MacBook Air 2024 M3

If they're running different OSs, then probably the best thing to do is to open a brand new Library on the M3Air (cool!) and let it populate from iCloud. It's easy and doesn't take any monitoring of the process by you. But don't be in a hurry! Leave the new computer plugged in and powered on, with Photos running in the background, every night until it's through.

The other way is to copy the Library to the new M3Air (lucky you!), either with an external drive or by connecting the macs together using "Target Disk Mode:" You may have to wait for the new computer to make the old Library compatible. Then force the downloading of originals by printing the entire library to a pdf (because printing requires the originals, and you can then delete the pdf) or by making a slideshow of the originals-- I've heard that works, too.

Transfer files between two Mac computers using target disk mode - Apple Support

The advantage of the first way (using iCloud) is that only good stuff will be transferred, with no chance of getting stuck by old corrupt files, and the Library will be sure to be compatible with your shiny new M3Air (wow!).

Let us know how it goes...

That's great! Glad it worked...