Let me see if I can deal with the first part: Photos is an application that is kept in the Applications folder and can be seen usually in the dock on a Mac. Photos contains instructions for using the data in the Photos Library.
The Photos Library has all the pictures and data, and it has a database that connects all that stuff so that the Photos app can make sense of it to us users. The default name of the Photos Library is "Photos Library.photoslibrary" This Library is normally kept in the user's Pictures folder.
The Photos Library must be directly connected to the computer-- it can't work if it's on a network of cloud or has to be accessed over the internet. So it can't work if it's locate in iCloud Drive. Sometimes, when people try to put the Library on a networked drive, it damages the Library. So, if you see it on Dropbox or One Drive or iCloud Drive, that's no good, and you should try to move it back to the Pictures folder.
Photos Library, like a folder, contains lots of files. But messing around inside of that folder can mess up the database's ability to keep track. So, the folder is protected a little bit, and if you try to open it, it gives a warning that you shouldn't. This "protected" folder is called a package. Sometimes people run unnecessary "cleanup" programs on their Macs, and they mess around inside the package and cause damage.
The Photos Library will work from pretty much anywhere on your Mac except iCloud Drive. By the way, in Sonoma, the iCloud Drive seems to be called Mobile Documents.
iCloud Drive is different from iCloud Photos, though each is used for synchronizing stuff between all a user's devices. For instance, iCloud Photos, when it's turn on, keeps the pictures on your Mac, on your iPhone, and on your iPad all exactly the same. Photos does this by copying pictures from the Mac to iCloud Photos Library, and then copying them to other devices, and vice versa. iCloud Drive does essentially the same for documents and files.
So, as with you, I'm trying to make sense of what you are saying. For instance,
- you say, "I only see one library on my iMac," but you don't say where or how big the files is or it's name.
- You say, "Photos in iCloud not showing up at all when I'm on my iMac 10.13.6," but I'm not sure what that means-- Photos in iCloud? Are you looking at iCloud Drive, iCloud Photos, in Safari, or a Photos Library on your drive?
- You say, "I "DO" see the photos if I login to iCloud on MBP running Monterey." Do you mean at iCloud.com? Do you see the ".photoslibrary" package on your MBP?
There's so much, here, that either of us may lose track. If we fail to get a solution, the next step is to go to Apple and allow them to log into your computer so that they can actually see what's going on. So, there is always hope!