[Enhancement] Add microphone capture helper for streaming transcription

[deepgram-robot]

Summary

Add a built-in microphone capture utility to the Python SDK that handles audio device enumeration, capture configuration, and streaming to Deepgram's live transcription WebSocket — eliminating the need for developers to separately install and configure PyAudio or sounddevice.

Problem it solves

Every developer building a live transcription demo in Python faces the same 30-minute setup hurdle: install PyAudio (which requires system-level portaudio headers), configure sample rate/channels/chunk size, write a capture loop, and pipe bytes to the Deepgram WebSocket. This friction is the #1 source of GitHub issues on the SDK (issues #425, #302, #418, #440, #495). A built-in helper would make "mic to transcript" a 5-line script.

Proposed API

from deepgram import DeepgramClient, Microphone

dg = DeepgramClient(api_key="...")
connection = dg.listen.websocket.v("1")

connection.on("transcript", lambda result: print(result.channel.alternatives[0].transcript))

connection.start({"model": "nova-3", "language": "en"})

mic = Microphone(connection.send)
mic.start()

# ... later
mic.finish()
connection.finish()

Alternatively, an even simpler context-manager pattern:

async with dg.listen.live(model="nova-3") as session:
    async with Microphone(session) as mic:
        async for transcript in session.transcripts():
            print(transcript.text)

Acceptance criteria

• Works cross-platform (macOS, Linux, Windows) with automatic backend selection
• Installable via optional dependency: pip install deepgram-sdk[microphone]
• Handles sample rate, channels, and chunk size configuration with sensible defaults
• Provides device enumeration (Microphone.list_devices())
• Documented with usage example
• Compatible with existing API (works with current ListenWebSocketClient)

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Raised by the DX intelligence system.