A true integration for Home Assistant would be the ‘cats meow’ (bad bird joke ) This might offer you something as a start. I wrote this rough Python program to send the ‘heard birds’ in BirdNET-Pi (or in my case a branch off that work that is running in a Proxmox VM) via MQTT to Home Assistant.
The BirdNET-Pi project and related work is a lot of fun. The code is a bit long in the tooth IMHO, but it works pretty well. I want to make a pass at simplifying the system, but that is one of many future TODO’s. For now, this code has been working pretty well and lets me see bird info in Home Assistant. You will have to poke around the code a bit to make changes to get it running in your environment, it does not currently have any ‘configuration’ files.