How do I reduce “Other System Data” storage on iPhone 12 mini?

"For example I noticed that "Other System Data" is taking up 15GB in my storage. I've seen suggestions on other posts about restarting the phone to rejig this, but that hasb't worked for me. It remains the same..."

You need to Back up the phone

Erase all content & settings

Set up the phone again, restoring the backup.

There is some risk so ensure you learn how to perform this.

Back up iPhone - Apple Support

Erase iPhone - Apple Support

Set up your iPhone or iPad – Apple Support (UK)

• Other: Non-removable mobile assets, like Siri voices, fonts, dictionaries, non-removable logs and caches, Spotlight index, and system data, such as Keychain and CloudKit Database. Cached files can't be deleted by the system.
• System: Space taken by the operating system. This can vary based on your device and model.

About cached files in "Other"

Finder and iTunes categorize cached music, videos, and photos as Other instead of actual songs, videos, or photos. Cached files are created when you stream or view content like music, videos, and photos. When you stream music or video, that content is stored as cached files on your device so you can quickly access it again.

Your device automatically removes cached files and temporary files when your device needs more space.

If storage on your device differs from what you see in Finder or iTunes

Since Finder and iTunes categorize cached files as Other, reported usage for Music or Videos might differ. To view usage on your device, go to Settings > General > [Device] Storage.

If you want to delete the cached files from your device

Your device automatically deletes cached files and temporary files when it needs more space. You don't need to delete them yourself.

In short --> IGNORE, if you are not convinced, Restart the device. You will see that Others Storage will reduce but total storage will remain more or less the same.

Watch the demo in the GIF below made on my iPhone 6 iOS 12.4.7

In short --> IGNORE, if you are not convinced, Restart the device. You will see that Others Storage will reduce but total storage will remain more or less the same

You may watch the same GIF in the form of Video on YouTube --> Others Storage consuming lot of space on an iPhone

"My 64 GB iPhone 12 mini is suffering - mostly because of the 33,000 photos and 2,500 videos I have on the device/iCloud. "

If you have sufficient iCloud paid for and Photos is set up to Optimise storage it should not be a problem.

IF you are sure all your media is in iCloud then restoring the phone as described above will restore only thumbnails to Photos