Does it also constitute a copyright infringement if I do not use the music commercially?

Yes, even the non-commercial use of copyright-protected music constitutes a copyright infringement if it takes place in public. According to Section 15(3) of the German Copyright Act (UrhG), use is deemed to be in public if the music is made available to a group of people who are not connected to one another or to the organiser through personal relationships. The decisive factor is not the intention to exploit the work commercially, but solely the public nature of the use. Private use within the family and among close friends, on the other hand, does not require authorisation. For all public use, you require a GEMA licence, regardless of whether you generate income from it.