Where are you seeing the message "Last update on my Mac shows 3/11 "? Are you seeing it as the "Date Modified" of the Photos Library? This date is rarely updated. What matters is is the status bar in Photos. You will see it, if you click "Library" in the Photos Sidebar, then the "Days" or "All Photos" tab. Below "All Photos" you will be seeing the state of the iCloud sync. Does it show "updated just now" or "Uploading ... items" or "Downloading ... items"?
For example, for me the status bar is showing this:

If the status should be showing "Uploading ... items", you will have to wait for the current upload to finish, before Photos for Mac can download the newer items from iCloud. The library on your Mac needs to be fully in sync with iCloud, before Photos can determine, which of the photos currently in iCloud are new and need downloading. If there are items listed as "Unable to upload" or "On this Mac only"; you have to find them and remove or replace them. They can make the upload hang.
Typically, Photos will start a new, complete upload into iCloud Photos, after the Photos Library has been repaired or rebuild after a system upgrade or a crash.