To back up old photos in iCloud, make sure iCloud sync is turned on. Go to Settings > Apple ID > iCloud > Photos > Depending on the device, turn on Sync this ...
Manually copy your library to an external storage device: Drag the photo library (stored by default in the Pictures folder on your Mac) to your storage device ...
I just use Photos and back up my Mac many different ways among three machines (Time Machine on all three, Chronosync on one, SuperDuper on one, Backblaze on ...
This article gives step-by-step instructions on how to backup photos on Mac using an external hard drive, your iCloud photo library, Google Drive or dedicated ...