Comment by nickthenerd

Technically Matter can run purely local, no external web requests (well there are some attestation and certs that are confirmed by the Controller). Then Matter devices use Endpoints and Clusters for control, device to device or Controller to device. Matter devices' Commissioning process is done in 2 ways - for Thread devices, they require the operational dataset of the Thread network, which is held by the Border Router, then the Border Router needs information about the Thread Device (Device ID, Discriminator, and PIN Code). This can be exchanged over BLE or NFC with the Controller (smartphone app like Homekit, Google Home, etc). If you have WiFi only devices then Commissioning is done via the Controller only. In both of these cases any DNS lookup would be done by the Controller.