Hi @Schlotheim, let me see if I can help out here!
I have translated your question to English as this is an International forum, please post any replies in English and it will be easier for me and other users to assist you.
Firstly I would like to ask you to check how old your SIM card is. Previous SIM card formats used different voltages. If your card is older than 4-5 years please contact your network operator to swap your SIM card. Another thing that you can try is to check if your Xperia device works with another SIM card to see if it is the SIM reader that is malfunctioning or if it is the SIM card that is malfunctioning.
Try this to begin with and feel free to keep me posted with the results!
