You said, "I thought choosing to push photos to iCloud would make them more accessible and reclaim space."
The base iCloud Photos is great for making photos and videos more accessible among your own devices with a common Apple ID. It can ease a storage crunch on a device if you make use of the "Optimize <device> Storage" option on that device, but there are tradeoffs.
Shared Library (as with the older Shared Albums) is for sharing photos and videos with other users.
Time Machine is great for local backup. iCloud Photos is not true backup at all; it is cross-device synchronization. If you delete a photo from your Mac, it will be deleted from iCloud and any other devices connected to the same iCloud Photos library. On the other hand, if the whole library is accidentally deleted outside Photos, you may be able to re-sync a copy from iCloud.
One of the tradeoffs of Optimize...Storage is that Time Machine cannot make a full backup of the photos that do not lie fully on your local Mac.