Ok, I figured this out! I’m on Home Assistant 2023.6.3, which is not the latest version (somehow the image/tag “homeassistant/raspberrypi3-homeassistant:stable” downloads that version instead of the latest one). So based on that, I had to downgrade Z2M to version 1.32.2, since newer versions require HA 2023.8.0. After downgrading, it works!
I found this information in the following related thread: Zigbee2mqtt and home assistant help - #9 by Tinkerer
Thanks for all the help!