Voice chat not working on Nintendo Switch

I bought a headset/mic (Turtle Beach Recon) which is specifically marketed as being compatible with Nintendo Switch. However when I try to use it on Apex, the audio comes through fine through the headphones but the game doesn't recognize that a mic is connected at all, so I can hear my teammates but they can't hear me.

I confirmed that the headset isn't muted or anything. I've also confirmed that the mic works fine on other consoles and on my computer. It is a wired headset with a 3.5mm jack, so I plug it into the headphone port on the top of the console. I've tried doing this in both handheld and docked modes but I get the same result - audio comes through the headset fine but the game doesn't recognize that a mic is connected.