Backup of the system photo library which is synced with iCloud

There may be some difficulty with keeping a Library on an external drive and also using iCloud on a MacBook. Plugging and unplugging the System Library might do bad things depending on what Photos is doing at the same time, and it will certainly cause time consuming re-syncing, as Photos has to check if anything has changed. Yesterday, for instance, I turned off iCloud for my Library (so I could do some stuff to another non-iCloud Library,) and when I reconnected, it took about 4 hours, I think, to re-sync. I hadn't actually changed anything, and my Library is on my internal drive.

I have an SSD that's USBc powered and weighs about 1 ounce. Very cute! If you only do the plugging when the Mac is off, it may work out. Another, probably better possibility is to keep the Library on the internal drive of the MacBook, but keep everything else on the small SSD. Then, no problems. That's how I use my little SSD; it goes with me and my computer. If your Library is still too large, you can divide it into two Libraries, Archive and a Favorites, and keep the smaller one on the computer and connected to iCloud.

I haven't figured out any way to backup a Library that is Optimized. Just downloading pictures from iCloud.com isn't really the same-- there's much more information in a Photos Library than what you get in downloaded pictures. I use "Optimized Storage" on my iPhone, but not on my Mac.

If your Library is synchronized with iCloud.com, then the pictures are always available through a browser with any computer any time anywhere. But there's not a lot that you can do with a browser--look, upload, download, choose favorites, play a slideshow-- not much else.

For backing up my pictures, I have two different drives, one HDD, the other SSD, on which I run Time Machine, roughly each every other day, more or less. Since I use a MacBook, they can't constantly connected. TM runs an incremental backup that allows you to look at each one years into the past. iCloud is my only off-site backup, but I hope that's OK in combination with the others.

You would be able to see an optimized photo when in iCloud, regardless of whether the SSD is still connected, but iCloud Photos is not a backup service, so you should definitely keep your photos on the SSD as a backup.

If you would like to have an external SSD that's small enough to easily take with you consider the 500GB, 1 TB or 2TB OWC Envoy Pro mini 

With it and a Time Machine backup schedule you could do away with the iCloud syncing.

The setup that you have is likely best. External drive for the library with a second drive as backup. You can optimize storage on the Mac and keep the library on the Mac but you then will not have the full resolution images on the Mac for backup. You can also access the library at iCloud.com.