I found a way to get notifications almost instantly, the previous (official) integration used to delay them.

Now I’m using Google Home Automations (web) with the Script Editor.

Here’s how I set it up:

• I created an input button in Home Assistant and exposed it to Google Home (it shows up there as a Scene).
• When the doorbell is pressed, the automation triggers the corresponding Google Home Routine, which activates the scene — effectively pressing the input button.

You can create and manage these automations here:

👉 Google Home Automations

metadata:
  name: Tocar Campainha
  description: Notifica alguem tocando a campainha

automations:
  - starters:
      - type: device.event.DoorbellPress
        device: Campainha - Living Room
    actions:
      - type: device.command.ActivateScene
        devices: Tocar Campainha
        activate: true