Sprint 6d — Migrate Gemini Live to @google/genai SDK

feat(geminiLive): rewrite with GoogleGenAI SDK (vertexai: true, apiKey)
  replaces raw WebSocket to generativelanguage.googleapis.com
feat(geminiLive): restore full setup config (systemInstruction,
  inputAudioTranscription, outputAudioTranscription, VAD)
fix(geminiLive): buildSetupFrame → SDK config object (no manual JSON)
fix(useT2LiveSession): cancelTokenRef for idempotent startDialogue,
  closeAllRef for stable unmount cleanup
chore: add @google/genai@^1.50.1 dependency
test: 11 geminiLive tests rewritten with SDK mock
  292/292 backend tests green

src/routes/t2live.ts

@@ -230,8 +230,8 @@ export async function runT2LiveCorrection(args: {
 }
 
 export interface CreateT2LiveRoutesOptions {
-  /** Injection pour les tests : fabrique de WebSocket vers Gemini. */
-  geminiFactory?: OpenGeminiLiveSessionOptions["geminiFactory"];
+  /** Injection pour les tests : fabrique de client SDK Gemini (Sprint 6d). */
+  clientFactory?: OpenGeminiLiveSessionOptions["clientFactory"];
   /** Injection pour les tests : override timeout/warning. */
   timeoutMs?: number;
   warningMs?: number;
@@ -313,7 +313,7 @@ export default function createT2LiveRoutes(
           openGeminiLiveSession(adapter, {
             role: sujetNonNull.role!,
             contexte: sujetNonNull.contexte!,
-            geminiFactory: opts.geminiFactory,
+            clientFactory: opts.clientFactory,
             timeoutMs: opts.timeoutMs,
             warningMs: opts.warningMs,
             onSessionEnd: async (transcript) => {