Sync Photo library between Photo application on two Macs using same Apple ID / iCloud account
I have two macs, a desktop and a MacBook Pro.
The system Photo library on the desktop is synced with iCloud -- so I can access those photos on the web through iCloud.com.
Is there really no way that the Photos app on my MacBook, with same iCloud account, can access the same library through iCloud? So, for example, when I open the Photos library on the MacBook I will see low-res versions that can be downloaded, edited, and synced via iCloud with the Photos library on the desktop Mac? And that photos I add to the Photos library on MacBook will be sync'd and available on the desktop Photos library ?
This seems like such a very useful and obvious functionality for iCloud, but I can't figure out how to implement it. Having to manually download photos through the web iCloud.com is unwieldy.
MacBook Pro 14″, macOS 12.3