Using the Apple lightning-to-USB C adapter to connect a lightning lavaliere mic to an iPhone 16 Pro

I have a Pixel Lavalier Microphone with a lightning connector. It works perfectly with my iPhone 11 Pro (just plug it in and record a video, and the iPhone uses the audio from the lavalier mic instead of the built-in mic). I also have the Apple USB-C to Lightning Adapter, but when I plug the adapter into the lavalier mic and then plug the adapter into my iPhone 16 Pro and record a video, the iPhone still uses the built-in mic from the iPhone for audio. The product page overview says that the adapter supports "charging, data, and audio", so I really do not know why this is not working.

Is there something I'm missing here? I was hoping not to have to buy a new lavalier mic with USB C.