Allow count_exceptions to add the error type as a label

I'd like count_exceptions to add the error type as a label so I can track what errors are occurring against what endpoints for my application.

I'd like to do this via the with method.

from prometheus_client import Counter

ERRORS = Counter(
    'http_request_errors_count',
    'Count of  exceptions that happen during an HTTP request',
    ['method', 'endpoint', 'error']
)

async def error_middleware(request, handler):
    try:
        with ERRORS.count_exceptions(request.method, request.path):
            return await handler(request)
    except SomeHTTPException as e:
        ...

To do this I've created my own custom Counter classes.

from prometheus_client import Counter, context_managers


class CustomExceptionCounter(context_managers.ExceptionCounter):
    def __init__(self, counter, exception, *labels):
        self._counter = counter
        self._exception = exception
        self._labels = labels

    def __exit__(self, typ, value, traceback):
        if isinstance(value, self._exception):
            self._counter.labels(*(*self._labels, typ.__name__)).inc()  # Append exception's name as a label


class CustomCounter(Counter):
    def count_exceptions(self, *labels, exception=Exception):
        return CustomExceptionCounter(self, exception, *labels)


ERRORS = CustomCounter(
    'http_request_errors_count',
    'Count of CancelledError exceptions',
    ['method', 'endpoint', 'error']
)

I think there is a general solution that's backward compatible, I've just not figured it out. Is this something you'd support? I'd be happy to submit a PR if I can figure out how to make this backward compatible.

Start with Counter.count_exceptions and context_managers.ExceptionCounter, then trace how the with method handles exception types and labels. Define how an error label can be added while preserving existing calls and behavior, and verify the requested endpoint and exception-label use case with tests for backward compatibility.