Hello Mathis Witte,
Welcome to the Microsoft Q&A forum.
Unfortunately, the Copy Activity in Azure Data Factory does not have an option to preserve the content-type of the files being copied. Currently, the 'Content-Type' properties of the file that were copied via ADF will be 'application/octet-stream'
As you mentioned, one possible solution to this problem is to use an Azure Function to update the content-type of the unzipped files after they have been copied to the destination blob storage.
This feature request has been logged in the ADF ideas forum.
https://feedback.azure.com/d365community/idea/6664d52e-5466-ed11-a81b-000d3ae49307
I would suggest upvoting and commenting on this feature request.
PG actively monitors and reviews all the feedback shared in this forum, prioritizing them accordingly based on the number of requests.
I hope this info helps. Please let me know if you have any further questions.