Hi Gandalf_sh,
Based upon the message that you're seeing, attempting to free up additional storage first would be recommended. If your iPhone or iPad won't update offers this:
"If there's not enough space to update
If there isn't enough space to download and install an update, the software on your device will try to make space. It will remove only app data that it can download again and doesn't remove or relocate any of your data. If your device still doesn't have enough space, you can use your computer to update your device.
If you can't connect your device to your computer, you can make room for the update by removing content and apps on your device that you don't use. Go to Settings > General > [Device name] Storage.
Learn more about the space your apps and content use."
Should this step still not resolve the matter, reach out to Apple Support directly to investigate further.
Regards.