One way to do this would be to make an api call with the requests library, and parse the JSON response:
import requests
url = 'https://maps.googleapis.com/maps/api/streetview?size=600x300&location=46.414382,10.013988&heading=151.78&pitch=-0.76&key=YOUR_API_KEY'
r = requests.get(url)
results = r.json()
error_message = results.get('error_message')
Now error_message will be the text of the error message (e.g., 'The provided API key is expired.'), or will be None if there is no error message. So later in your code you can check if there is an error message, and do things based on the content of the message:
if error_message and 'The provided API key is invalid.' in error_message:
do_something()
elif ...:
do_something_else()
You could also check the key 'status' if you just want to see if the request was successful or not:
status = results.get('status')