iOS Lightroom not syncing correctly

Hello @.bash

AlexJz is correct in that adding photos to album, and then setting Store Locally is a way of maintaining original images in Lightroom's app cache.  If that's what you want to do, be sure to toggle off "Only download smart previews" in the app's Settings > Cloud storage & Sync.  You may also want to adjust the local app cache size if you plan to keep lots of orginal images locally -- this is in Settings > Local storage > Cache size limit

The paid version of Lightroom mobile is designed to upload original images to the cloud and keep only downsampled copies locally (called Smart Previews).  This is intended to help the user save local storage space on the mobile device.  As long as you are online, original images can be downloaded on-demand.  The other option is the use of Store Locally for albums mentioned above.  I use this mostly when I want to be able to do extensive edits on photos when I know I won't have internet access for a while.  Otherwise, uploading imported originals and fetching them when needed works well for me.  I usually only need access to the original when I want to export at full resolution for sharing or printing.

Ah great thanks so much

For each album, you need to make them available offline actually.

Click on the "..." next to the album and enable "Store Locally".

"Synced and backed-up" just means that new pictures were uploaded to the cloud, and that every album that was enabled to be offline has been downloaded.