fix: use publishVersion for SnapStart Java in auth test

forceColdStart uses UpdateFunctionConfiguration which doesn't work on
qualified ARNs. Use publishVersion + waitForSnapStartReady instead,
matching the pattern from snapstart.test.ts.

Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>

Author: jchrostek-dd

integration-tests/tests/auth.test.ts

@@ -1,6 +1,6 @@
 import { invokeAndCollectTelemetry, FunctionConfig } from './utils/default';
 import { DatadogTelemetry } from './utils/datadog';
-import { forceColdStart } from './utils/lambda';
+import { forceColdStart, publishVersion, waitForSnapStartReady } from './utils/lambda';
 import { getIdentifier } from '../config';
 
 const identifier = getIdentifier();
@@ -12,13 +12,19 @@ describe('Auth Integration Tests', () => {
   const getFirstInvocation = (runtime: string) => telemetry[runtime]?.threads[0]?.[0];
 
   beforeAll(async () => {
+    const nodeFunctionName = `${stackName}-node`;
+    const javaFunctionName = `${stackName}-java`;
+
+    await forceColdStart(nodeFunctionName);
+
+    const javaVersion = await publishVersion(javaFunctionName);
+    await waitForSnapStartReady(javaFunctionName, javaVersion);
+
     const functions: FunctionConfig[] = [
-      { functionName: `${stackName}-node`, runtime: 'node' },
-      { functionName: `${stackName}-java:snapstart`, runtime: 'java' },
+      { functionName: nodeFunctionName, runtime: 'node' },
+      { functionName: `${javaFunctionName}:${javaVersion}`, runtime: 'java' },
     ];
 
-    await Promise.all(functions.map(fn => forceColdStart(fn.functionName)));
-
     telemetry = await invokeAndCollectTelemetry(functions, 1);
 
     console.log('All invocations and data fetching completed');