The socket on the mute is a microphone output jack not a headphone output jack, which is why you need the personal studio box in-between the mute and your headphones.
FWIW, I bought the Yamaha Silent Brass PM7 (mute) + ST7 (personal studio) for my trumpet years back, and although I still use the physical mute every day when I practise at home, I long ago ...
You need the other half too :\
Clearest response from the Q&A section on Yamaha PM7X SILENT Brass Pickup Mute for Trumpet & Cornet
The PMX Series Silent Brass Pickup Mutes aren't designed for use
without the SBX2 Personal Studio. If you don't already have an SBX2,
we'd advise choosing the SB7X Silent Brass Kit for Trumpet and Cornet
- this ...