My Photos app on my Mac hasn't been syncing properly with iCloud since the Monterey Update

OK - we may be on to something.

Sometimes those unable to upload items can block the sync process. You need to export them from photos to a folder, convert them to a compatible format, then delete from photos and re-import the compatible versions.

Also check the smart album I suggested.

Also worth answering the questions from Leonie below. And see her user tip about weeding out legacy media

How to Weed out Legacy Media in Photos fo… - Apple Community

The free storage is looking good, then.

The system version would have been helpful, if you upgraded from a system that still has been supporting 32-but applications. In that case you might have been running a system version that supported legacy formats for media files(About legacy media in iMovie for macOS - Apple Support).

For the "unable to upload" items you may want to look at this support document "Check the status of your library in Photos for macOS - Apple Support" to follow Tony's suggestion of exporting and reimporting. The problematic items need to be removed completely from the library, including "Recently Deleted", before you reimport them.

In my library the most recalcitrant items blocking the upload have been PDF images, very old videos, Live Photos created with third party apps, externally edited photos with unsupported color sync profiles.

Where is your local library package? As well as being in iCloud it is synced to your mac. By default in the pictures folder, but with a library this size you may have it on an external drive. You can see where it is in preferences:

Do you have an "unable to upload" folder in the app. Or if you create a smart album with the condition "photos - is unable to upload" does it show anything?

I'm guessing that your upgrade to Monterey has triggered a complete new sync with iCloud - if your library is large this can take many days (or even weeks) even with the Mac on 24/7, so it may just be a case of letting it get on with it, leaving your mac on 24/7 with sleep disabled.

However, if your library is in an unsupported location (eg an external drive NOT formatted APFS or MacOS extended - or on a network drive, or on a synced drive like dropbox) then that may prevent the sync working correctly.

What does the sync status say at the bottom of the all photos view?

Which system version did you have installed before the upgrade to Monterey?

How much free storage is on your Mac and in iCloud?