You should use an always-on VPN if you want to minimize the fingerprintable network traffic of the device. If an always-on VPN is not used, a network operator will be able to see DNS requests and TLS metadata for various GrapheneOS connections (releases.grapheneos.org for OS updates, apps.grapheneos.org for app updates, etc.). If the VPN is used, the network operator will see a VPN connection instead of many more unique, individual connections.
A cellular connection will reveal all of the same network traffic described above by de0u. If a VPN is used with a cellular connection, there are similar benefits to hiding the individual network connections. Additionally, your phone's IMEI is revealed to the carrier, which uniquely identifies your phone. The IMEI reveals the device model of the phone.
Cellular connectivity is inherently more invasive, so you'll never be able to fully hide your device from a cellular operator.