Do I need a splitter that supports a microphone, or audio-only is enough?

For call center training, you definitely need a splitter that supports a microphone. Even if the supervisor only intends to listen, the trainee must be able to speak to the customer. If you use an audio-only splitter, it might cut off the microphone signal entirely, meaning the customer won't hear anyone. Always look for a headset mic splitter or a purpose-built training cable.