There are a couple issues like this on the swift-matter-examples repo. I don't have an esp32-c6 anymore handy to try to root cause so any help would be awesome.
I have the same issue
my setup:
Macos Sequoia
Swift DEVELOPMENT-SNAPSHOT-2024-06-13-a
ESP-IDF 5.2.1
ESP-Matter 1.2
ESP32-C6
Pairing with an iPhone 15 Pro to HomeKit with a Homepod Mini
and i got the same log as well, exactly the same
I don't think there is any public information or examples on Matter on Pico W. It's probably a lot of non-trivial work, and it's not clear whether the hw specs would make it even possible at all.