Is there a way to move a Photos project from one computer to another?

Projects can only be transferred as part of a Photos Library.

• Copy the Photos Library from your laptop to an external drive (the file system format of the drive needs to be MacOS Extended (Journaled). Set the "Ignore Ownership on ths volume" flag to avoid permission problems as described here: Sharing photo libraries among multiple users - Apple Support
• Open the copy of the library on the external drive and delete all photos, that are not used for your card project. Empty the "Recently Deleted" album.
• Then copy the library from the external drive to your desktop computer.

Double click the library on the Desktop computer to open it in Photos.

Not except by transferring the library as projects do not exist separate from the library - you may want to duplicate the library and then use Photos to delete everything except the project ad its photos so you can transfer just the bare minimum sized library to the other computer

And once you modify the project on the other computer there is no way to get it back into your main library on the first computer

LN

You may want to tell the developers what you want - use this link: Feedback - Photos - Apple

But until Apple changes this, it is best to create each new project in a separate Photos Library for two reasons:

• Small libraries can be transferred between your devices on a thumbs drive and easily backed up.
• And more important - you are less likely to accidentally delete photos from the library that are needed for your book or slideshow. Right now it is difficult to tell, if a photo is used in a project, when you try to delete duplicates and remove photos to save storage.