Vercel ai gateway (#7)

* feat: use vercel ai gateway

* chore: update UI

utils/aiGatewayClient.ts

@@ -0,0 +1,54 @@
+import { generateText } from 'ai';
+
+interface AiGatewayResponse {
+  text: string;
+  tokensUsed: number;
+}
+
+export async function queryAiGateway(
+  text: string,
+  model: string
+): Promise<AiGatewayResponse> {
+  const requestId = Math.random().toString(36).substring(7);
+  const startTime = Date.now();
+
+  console.info(`[AI-${requestId}] Starting Vercel Gateway AI request`, {
+    promptLength: text.length,
+    model,
+    timestamp: new Date().toISOString()
+  });
+
+  try {
+    const response = await generateText({
+      model,
+      prompt: text
+    });
+
+    const duration = Date.now() - startTime;
+    const tokensUsed = response.usage?.totalTokens || 0;
+
+    console.info(
+      `[AI-${requestId}] Vercel Gateway AI response received in ${duration}ms`,
+      {
+        responseLength: response.text.length,
+        tokensUsed,
+        usage: response.usage
+      }
+    );
+
+    return {
+      text: response.text,
+      tokensUsed
+    };
+  } catch (error) {
+    const duration = Date.now() - startTime;
+    console.error(
+      `[AI-${requestId}] Vercel Gateway AI error after ${duration}ms:`,
+      {
+        error: error instanceof Error ? error.message : String(error),
+        promptLength: text.length
+      }
+    );
+    throw new Error(`Vercel Gateway AI error: ${JSON.stringify(error)}.`);
+  }
+}