feat: Proxy extensions — audio, video, completions, embeddings

- Generic execute_proxy_request executor for arbitrary paths
- POST /v1/completions, /v1/embeddings
- POST /v1/audio/speech, /v1/audio/transcriptions, /v1/audio/translations
- POST /v1/videos
- All reuse existing auth + route resolution infra
- 18/18 tests pass

boosapi-rs/src/routes/proxy/mod.rs

@@ -47,7 +47,11 @@ pub fn routes() -> Router<AppState> {
         .route("/v1/chat/completions", post(chat_completions))
         .route("/v1/completions", post(completions_handler))
         .route("/v1/embeddings", post(embeddings_handler))
+        .route("/v1/audio/transcriptions", post(audio_transcriptions))
+        .route("/v1/audio/translations", post(audio_translations))
+        .route("/v1/audio/speech", post(audio_speech))
         .route("/v1/images/generations", post(images_generations))
+        .route("/v1/videos", post(videos_handler))
         .route("/v1/models", get(list_models))
 }
 
@@ -126,6 +130,89 @@ async fn embeddings_handler(
     Ok(Json(result))
 }
 
+/// POST /v1/audio/speech
+async fn audio_speech(
+    State(state): State<AppState>,
+    headers: HeaderMap,
+    Json(body): Json<Value>,
+) -> AppResult<Json<Value>> {
+    info!("POST /v1/audio/speech");
+
+    check_auth(&state, &headers).await?;
+
+    let model = body
+        .get("model")
+        .and_then(|m| m.as_str())
+        .ok_or_else(|| AppError::BadRequest("model is required".into()))?
+        .to_string();
+
+    let route = resolve_route(&state, &model).await?;
+    let result = executors::execute_proxy_request(state, route, "/audio/speech", body).await?;
+    Ok(Json(result))
+}
+
+/// POST /v1/audio/transcriptions — proxy to upstream
+async fn audio_transcriptions(
+    State(state): State<AppState>,
+    headers: HeaderMap,
+    Json(body): Json<Value>,
+) -> AppResult<Json<Value>> {
+    info!("POST /v1/audio/transcriptions");
+
+    check_auth(&state, &headers).await?;
+
+    let model = body
+        .get("model")
+        .and_then(|m| m.as_str())
+        .ok_or_else(|| AppError::BadRequest("model is required".into()))?
+        .to_string();
+
+    let route = resolve_route(&state, &model).await?;
+    let result = executors::execute_proxy_request(state, route, "/audio/transcriptions", body).await?;
+    Ok(Json(result))
+}
+
+/// POST /v1/audio/translations — proxy to upstream
+async fn audio_translations(
+    State(state): State<AppState>,
+    headers: HeaderMap,
+    Json(body): Json<Value>,
+) -> AppResult<Json<Value>> {
+    info!("POST /v1/audio/translations");
+
+    check_auth(&state, &headers).await?;
+
+    let model = body
+        .get("model")
+        .and_then(|m| m.as_str())
+        .ok_or_else(|| AppError::BadRequest("model is required".into()))?
+        .to_string();
+
+    let route = resolve_route(&state, &model).await?;
+    let result = executors::execute_proxy_request(state, route, "/audio/translations", body).await?;
+    Ok(Json(result))
+}
+
+/// POST /v1/videos — list/create video generation tasks
+async fn videos_handler(
+    State(state): State<AppState>,
+    headers: HeaderMap,
+    Json(body): Json<Value>,
+) -> AppResult<Json<Value>> {
+    info!("POST /v1/videos");
+
+    check_auth(&state, &headers).await?;
+
+    let model = body
+        .get("model")
+        .and_then(|m| m.as_str())
+        .unwrap_or("default");
+
+    let route = resolve_route(&state, model).await?;
+    let result = executors::execute_proxy_request(state, route, "/videos", body).await?;
+    Ok(Json(result))
+}
+
 /// POST /v1/images/generations
 async fn images_generations(
     State(state): State<AppState>,