The lightbulbs probably don't directly have Wi-Fi and communicate with the remote server, therefore probably support local protocols such as BLE, Z-Wave, Zigbee

The lightbulbs probably don't directly have Wi-Fi and communicate with the remote server, therefore probably support local protocols such as BLE, Z-Wave, Zigbee, therefore it's probably possible someone has reverse engineered them already (even if they don't have a local-only mode). Take a look at projects such as Home Assistant, they enable a fully local experience.