How to obtain Google Cloud Run service URL with Python

Question

I would like to obtain the URL of my Cloud Run service programmatically so I only need to hard code the name of the service and not its URL. This is so I can have the same code deployed in my test and production environments without having to access this value as a secret.

I'm currently trying the cloud run package as:

from google.cloud.run_v2.services.services.client import ServicesClient

def get_service_url(service):
    project_number = '123456789'
    location = 'europe-west2'
    service_name = f'projects/{project_number}/locations/{location}/services/{service}'
    ServicesClient.get_service(name=service_name)

get_service_url('my_service')

However this returns

    Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: __init__() got an unexpected keyword argument 'name'
>>> run_client.ServicesClient.get_service(name=service_name)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: get_service() missing 1 required positional argument: 'self'
>>> run_client.ServicesClient().get_service(name=service_name
Traceback (most recent call last):
  File "\lib\site-packages\google\api_core\grpc_helpers.py", line 67, in error_remapped_callable
    return callable_(*args, **kwargs)
  File "\lib\site-packages\grpc\_channel.py", line 946, in __call__
    return _end_unary_response_blocking(state, call, False, None)
  File "\lib\site-packages\grpc\_channel.py", line 849, in _end_unary_response_blocking
    raise _InactiveRpcError(state)
grpc._channel._InactiveRpcError: <_InactiveRpcError of RPC that terminated with:
        status = StatusCode.UNIMPLEMENTED
        details = "Operation is not implemented, or supported, or enabled."
        debug_error_string = "{"created":"@1649862914.759000000","description":"Error received from peer ipv4:142.250.184.234:443","file":"src/core/lib/surface/call.cc","file_line":904,"grpc_message":"Operation is not implemented, or supported, or enabled.","grpc_status":12}"
>

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "\lib\site-packages\google\cloud\run_v2\services\services\client.py", line 781, in get_service
    response = rpc(
  File "\lib\site-packages\google\api_core\gapic_v1\method.py", line 145, in __call__
    return wrapped_func(*args, **kwargs)
  File "\lib\site-packages\google\api_core\retry.py", line 286, in retry_wrapped_func
    return retry_target(
  File "\lib\site-packages\google\api_core\retry.py", line 189, in retry_target
    return target()
  File "\lib\site-packages\google\api_core\grpc_helpers.py", line 69, in error_remapped_callable
    six.raise_from(exceptions.from_grpc_error(exc), exc)
  File "<string>", line 3, in raise_from
google.api_core.exceptions.MethodNotImplemented: 501 Operation is not implemented, or supported, or enabled.