The easy way: take your existing wiring. Put an 18VAC to 5VDC power supply in parallel with the pushbutton. Then, the output of that power supply goes to the 5V USB input of your camera setup.

The downside is that it will reboot the camera every time someone rings the doorbell, because you are shorting across the camera’s power supply.

You can put a resistor in series with the button to fix this. You will need to find a resistance that’s low enough to still cause the chime to ring, but high enough not to disrupt the camera’s power supply. Maybe start around 20 ohms. If you can’t find a working resistor value, you can change the transformer to a 24V or 36V transformer, but make sure to keep that resistor high enough not to burn out the chime, and make sure your 5VDC power supply can handle the increase in input voltage.