[Enhancement] Add Text-to-Speech WebSocket streaming support

[deepgram-robot]

Summary

Add TTS WebSocket streaming support to the Rust SDK, enabling real-time text-to-speech audio generation. This would allow Rust developers to stream text to Deepgram and receive audio chunks in real-time, essential for voice agent and interactive applications.

Problem it solves

Rust developers building low-latency voice applications (game engines, embedded systems, real-time communication servers) need streaming TTS for interactive speech synthesis. The Rust SDK currently has an open issue (#95) for TTS WebSocket support but no implementation. TTS REST is available but doesn't support streaming, which is required for real-time voice agent use cases where audio needs to start playing before the full response is generated.

Proposed API

use deepgram::tts::{TtsWebSocket, TtsOptions, TtsEvent};

let options = TtsOptions::builder()
    .model("aura-2-en")
    .encoding(AudioEncoding::Linear16)
    .sample_rate(16000)
    .build();

let mut tts_ws = deepgram.tts().websocket(options).await?;

// Send text for synthesis
tts_ws.send_text("Hello, how can I help you today?").await?;
tts_ws.flush().await?;

// Receive audio chunks
while let Some(event) = tts_ws.next().await {
    match event? {
        TtsEvent::Audio(data) => { /* play or forward audio bytes */ },
        TtsEvent::Flushed => { /* all audio for current text received */ },
        TtsEvent::Warning(msg) => { /* handle warning */ },
    }
}

Acceptance criteria

• TTS WebSocket client with streaming text input and audio output
• Support for flush and close operations
• Typed event handling (Audio, Flushed, Warning, Close)
• Documented with usage example
• Compatible with existing SDK async architecture (tokio)
• Includes example in examples/ directory

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Raised by the DX intelligence system.

[dg-coreylweathers]

Implemented in #166 (Phase 3): streaming Text-to-Speech over a WebSocket. Speak::speak_stream() opens a session (SpeakStreamHandle) with speak/flush/clear/close and a futures::Stream of SpeakResponse (audio + Metadata/Flushed/Cleared/Warning). Live-verified against production. Will close when v0.11.0 lands on main.