feat(geminiLive): restore systemInstruction in setup frame

src/lib/geminiLive.ts

@@ -214,13 +214,16 @@ function tryParseGeminiJson(data: unknown): GeminiServerMessage | null {
  * `realtimeInputConfig.automaticActivityDetection` sont volontairement
  * retirés tant que `setupComplete` n'est pas confirmé en prod.
  */
-function buildSetupFrame(): string {
+function buildSetupFrame(systemPrompt: string): string {
   return JSON.stringify({
     setup: {
       model: `models/${GEMINI_LIVE_MODEL}`,
       generationConfig: {
         responseModalities: ["AUDIO"],
       },
+      systemInstruction: {
+        parts: [{ text: systemPrompt }],
+      },
     },
   });
 }
@@ -256,12 +259,10 @@ export function openGeminiLiveSession(
 
   const timeoutMs = opts.timeoutMs ?? T2_SESSION_TIMEOUT_MS;
   const warningMs = opts.warningMs ?? T2_SESSION_WARNING_MS;
-  // Conservé en signature pour usage futur (réintégration `systemInstruction`).
-  const _systemPrompt = buildT2SystemPrompt({
+  const systemPrompt = buildT2SystemPrompt({
     role: opts.role,
     contexte: opts.contexte,
   });
-  void _systemPrompt;
 
   const url = `${GEMINI_LIVE_URL}?key=${apiKey}`;
   const factory =
@@ -312,7 +313,7 @@ export function openGeminiLiveSession(
 
   geminiWs.on("open", () => {
     console.log("[T2] Gemini WS open");
-    const frame = buildSetupFrame();
+    const frame = buildSetupFrame(systemPrompt);
     console.log("[T2] Gemini setup frame:", frame);
     try {
       geminiWs.send(frame);