I have a paid subscription to Lightroom for an iPad (2020). It syncs well to the cloud it seems. However it doesn't seem to store locally. In my albums I have chosen the option to store locally. In each album, it shows a small blue V sign indicated that the local storage option is activated. But when I view the 'local storage' heading in my settings, it says 0 GB is reserved for local storage. What is going on?
Trying this on my own iPhone and iPad, I can't reproduce any problem. Enabling Store Locally on any album increments the amount of local device storage used, whether I try with a clean install on my device, or also if I import a few dozen images from my camera roll straight into a Stored Locally album.
Are you certain your files are indeed synced up fully to cloud storage? If you sign into your same account on another iOS or Android device, do you see all your expecteed files? You can also check by signing into our Lightroom Web app in any browser at https://lightroom.adobe.com
If your files are indeed uploaded, and Lightroom shows "Synced and Backed Up" when you tap the cloud icon, does it help if you force quit and relaunch the app?
Another thing I wonder: in Lightroom app Settings > Cloud Storage & Sync, is the setting "Only Download Smart Previews" enabled? This is enabled by default, and will only sync down Smart Previews which are smaller copies of your images, often much smaller in file size compared to original images. When I tried Store Locally on an album with only 10 images in it, Local Storage used for me was 0.01 GB though the original RAW images amount to 0.25 GB. I actually recommend leaving "Only Download Smart Previews" enabled as this takes up much less device storage while still giving you high quality images to edit.
If none of my thoughts here help or don't explain what you're seeing, please write back. Also, it couldn't hurt to make a full iTunes or iCloud backup of your device. This will allow you to try other troubleshooting ideas like re-installing the app while also ensuring your can restore your device and files within your local Lightroom app as they are today.