Any and all data gathered through the usage of the TeamSpeak Server software (including, but not limited to, log files, IP addresses etc.), the storage and usage of said data is your responsibility, respectively those of the admins of the server, as these have the sole access to that data.
Privately run servers, may not be suspect to GDPR laws (see Article 2, Section 2 c GDPR). This exemption is void if any commercial activity is conducted, regardless of whether money is involved. This includes advertisements, exchange of data for services, etc. The exemption is also not applicable if you make any private data accessible to the public. Public collections of data are always suspect to GDPR law.
This answer does not constitute legal advice and does not replace it. If you have any further questions, a lawyer or data protection officer should be consulted.
When sending PMs please make sure to include a reference link to the thread in question in the body of your message.