It sounds like your HomeKit setup may have Sound Recognition enabled with sensitivity that's picking up your bird's beeps and whistles as smoke or CO alarms. This seems to be a fairly common issue since the recent update expanded sound detection capabilities on HomePod and other listening devices.
Here's how to adjust or disable it:
On your iPhone or iPad:
- Open the Home app
- Tap the ⋯ (three dots) in the upper right corner
- Select Home Settings
- Tap Safety & Security (or Sound Recognition depending on your iOS version)
- From here, you can either turn off Sound Recognition entirely, or disable it on specific HomePods/devices that are in the same room as your parrots
Alternative option:
If you'd like to keep Sound Recognition on in other parts of your home, you can go into each HomePod's individual settings in the Home app and toggle "Recognize Sounds" off for just the rooms where your parrots live.
You may also want to check whether the alerts are coming from a specific accessory (like a HomePod mini in the bird room)
Unfortunately there isn't currently a way to "train" HomeKit to ignore specific sounds, but hopefully Apple will add more granular controls in a future update. You can submit that as feedback here: feedback.apple.com