As mentioned by @Carcigenicate and @AzyCrw4282 in the comments connect is not called automatically. Though i am still unsure how websockets connect if connect is not called automatically because i could see messages coming. Anyways i have made the following changes and after making these changes i was able to see transcription in console.

config = types.RecognitionConfig(
                                   encoding=enums.RecognitionConfig.AudioEncoding.MULAW,
                                   sample_rate_hertz=8000,
                                   language_code='en-US'
                                 )

streaming_config = types.StreamingRecognitionConfig(config=config,interim_results=True)


def on_transcription_response(response):
    if not response.results:
        return

    result = response.results[0]
    if not result.alternatives:
        return

    transcription = result.alternatives[0].transcript
    print("Transcription: " + transcription)


bridge = None

def set_bridge():
    global bridge

    if bridge is None:
        bridge = SpeechClientBridge(streaming_config,on_transcription_response)


class MediaStreamConsumer(WebsocketConsumer):

    def connect(self, message, **kwargs):
        self.message.reply_channel.send({"accept": True})


    def raw_receive(self, message, **kwargs):
        set_bridge()

        data = json.loads(message['text'])

        if data["event"] in ("connected", "start"):
            print(f"Media WS: Received event '{data['event']}': {message}")
        
        if data["event"] == "media":
            media = data["media"]
            chunk = base64.b64decode(media["payload"])

            bridge.add_request(chunk)
   
        if data["event"] == "stop":
            print(f"Media WS: Received event 'stop': {message}")
            print("Stopping...")


    def disconnect(self, message, **kwargs):
        bridge.terminate()