Make iCloud Photos work PLEASE

I am experiencing the unexplainable with iCloud Photos. I recently purchased the iCloud+ 2TB subscription, and activated iCloud Photos on both my MacBook and iPhone, as well as Advanced Protection. Since then, nothing went right:

• My iPhone took 2 days to synchronize my photos to iCloud
• My Mac does not display, in Library, the same photos than on my iPhone
• I cannot access iCloud Photos on my browser on Mac anymore: it will require that I allow access from my iPhone, and once done, it fails and says it "Cannot Display Your Photos"

ChatGPT tells me there's something about "System Photo Library". It advises me to import all my photos to my Mac, then to make it my System Photo Library, then to synchronize it with iCloud.

Problem: the "Use as System Photo Library" is greyed out and cannot be clicked on. What's more, even if I succeeded, I don't have the guarantee that the photos I take with my iPhone will be displayed on my Mac, as the Mac will be master, and the iPhone the slave.

ChatGPT then tells me that the other option is to make my iPhone the "System Photo Library", and advises me to import all my photos to my iPhone, then to synchronize it with iCloud.

Problem: my iPhone definitely does not have enough storage for that!

And I still don't have any idea why my access to iCloud Photos is now denied.

I am stuck! This 10$ subscription is giving me more pain than solution so far.

Thanks for your help