System files taking up more than half of the phone

My System Data only takes up roughly 13 GB on my iPhone, so that does sound abnormal. You may have some corrupt data on your iPhone. So the very first thing you should do is a Forced Restart, as the procedure is shown below.

• Press and quickly release the volume up button.
• Press and quickly release the volume down button.
• Press and hold the side button until you see the Apple logo 

If that doesn’t help, the next thing to do is to backup your iPhone, then erase and restore it. The support article below explains how to perform it.

Restore your iPhone, iPad or iPod touch from a backup – Apple Support (AU)

Sz4fka wrote:

after restarting my phone only gets around 500mb more free space, but after a few hours it takes up the freed space again. However I’ve never heard of the second option you told me and it seems very promising, so I’ll try it and if anything goes wrong I’ll let you know. Thanks

Do keep us posted!

Sz4fka wrote:

So I need to make a backup on iCloud, right? Will 5 GB be enough for the files? And also how do I check if I have a backup already?

Go to Settings > [your name] > iCloud > iCloud Backup > Back Up Now. Wait until it is complete then go to Settings > General > Transfer or Reset iPhone > Erase all Content and Settings. Lastly when you see the Hello screen, go through the setup again and tap Restore from iCloud Backup and select your most recent one you just did.