Is it possible to write script functions (in the load script) one time in a certain place and use them (via some kind of import) for different apps without copying the same code into the app?
Is there a way to manage it globally and use it across different apps?
I think you're looking for the Qlik Deployment Framework.
You can use the Include directive to include a text file (with for example script code) in your apps script. See the online help for more information: Include ‒ Qlik Sense
You do not need QDF to be able to use Include. But QDF makes it a lot easier to reuse code and other resources in apps. And yes, QDF can also be used with Qlik Sense.