You can see the instructions for this connection using this instruction link
The Apple HomePod mini and Philips Hue Bloom Lamp can communicate with each other using a bridge. This bridge is necessary because there is no shared connection between the two devices.
With the Philips Hue Smart Hub, The Philips Hue Bloom Lamp's Wi-Fi can connect to the bridge, and the bridge can connect to the Zigbee connection of the Philips Hue Bloom Lamp. The Philips Hue Smart Hub also has Apple HomeKit compatibility, ensuring the connection can be made.
Another compatiblity is to use the connections between the third party Samsung SmartThings Hub 3rd Generation with the Philips Hue Bloom Lamp. This method can use the bridge to connect to the Zigbee connection of the Philips Hue Bloom Lamp. The Samsung SmartThings Hub 3rd Generation also has Apple HomeKit compatibility, allowing all of the devices to communicate to each other.
Interface Compatibility
 Apple HomePod mini |
 Philips Hue Smart Hub * Bridge required |
 Philips Hue Bloom Lamp |
|
|---|---|---|---|
| Amazon Alexa | No | Yes | Yes |
| Apple HomeKit | Yes | Yes | Yes |
| Google Assistant | No | Yes | Yes |
Connection Compatibility
|
Apple HomePod mini |
Philips Hue Smart Hub * Bridge required |
Philips Hue Bloom Lamp |
|
|---|---|---|---|
| Amazon Sidewalk | No | No | No |
| Bluetooth | Yes | No | No |
| Clear Connect | No | No | No |
| Thread | Yes | No | No |
| Wi-Fi | Yes | Yes | No |
| Z-Wave | No | No | No |
| Zigbee | No | Yes | Yes |