Restore my iPad mini 2, now the system is taking up 15.95GB of my 16GB

As a first step, perform a full reset of your iPad:

Settings > General > Reset > Erase All Content & Settings

Your iPad will reset and restart - after which you can proceed with setup of the iPad from the initial “screen”. Sign-in with your AppleID - but do not restore your backup to your iPad during setup. The objective at this stage is to complete a clean setup - and then to assess your available storage.

After initial setup, check your available local storage:

Settings > General > iPad Storage

Consider that a 16GB model will always struggle with available storage - as devices with only 16/32GB internal storage are not intended to keep very much data on the device itself. Of your initial 16GB, around half of this will be used just to store the iOS and built-in Apps - leaving very little for downloaded Apps and associated data.

With this consideration in mind, if all appears as expected, you can attempt to restore your backup to the iPad:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If your restored backup fills your available storage, your only option is to better manage the storage that you have - and delete unused Apps or unneeded data. 

These support pages should prove to be helpful:

About storage on your device and in iCloud – Apple Support

What's the difference between device storage and iCloud storage? – Apple Support

Manage your iCloud storage – Apple Support

How to check the storage on your iPhone, iPad and iPod touch – Apple Support

Clear Other storage on your iPhone or iPad - Apple Support

“Offloading” Apps can be a helpful method of creating temporary additional space.

https://9to5mac.com/2020/01/21/how-to-offload-apps-in-ios-to-save-space-without-deleting-their-data/

Additional information about creating sufficient space for installation of a software update can be found here:

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

External storage options can often help with managing limited internal storage. To do so, as your iPad has a Lightning port, you’ll need an Apple Lightning to USB3 Camera Adapter:

• Lightning to USB 3 Camera Adapter

https://store.apple.com/uk/xc/product/MK0W2ZM/A

System storage includes a lot of cached data. Reported System Data (a.k.a. “other data”) can be expected to fluctuate. Your iPad will automatically and optimally manage its available system resources, using available free space to cache data and improve overall performance.

The only element of system storage that you can directly influence is perhaps your browser caches - which you can manually clear if you wish to do so.

For Safari:

Settings > Safari > Clear History & Website Data

For other browsers, you’ll need to find the relevant section of the App settings - which may be within the App itself.

Otherwise, transient system caches can be significantly reduced by performing a forced-restart of your iPad - although caches, by their nature, will again accumulate and be automatically managed by the operating system.