Q: Does iCloud Photo Library sync projects

See this Support page:  Use Photos and iCloud Photo Library on multiple Mac computers - Apple Support

Projects do not sync with iCloud:

These items are available only on the Mac where you created them:

• Books, cards, and calendars
• Slideshows
• Keyword shortcuts
• Unused keywords
• Last imported album (this album contains photos you most recently imported on a specific Mac)
• Faces tiles and Faces data