Attempted to setup MQTT feeds for alerts from Blue Iris to Home Assistant this afternoon. It appears a single MQTT message was generated, which lacked the camera name in the MQTT topic. It was supposed to look like this.
I use MQTT for other purposes in Home Assistant, so I'm troubleshooting using the MQTT Explorer program. Only the single message with a BlueIris topic of "BlueIris/Alert" was ever received. After that, no more. 
Blue Iris version: 5.6.7.1 x64 (12/21/2022)
Code:
MQTT Topic: BlueIris/&NAME/Alert
Post/Payload: {"type":"Connectivity","trigger":"OFF"}

Blue Iris version: 5.6.7.1 x64 (12/21/2022)