Add workload identity federation support to base-action (#1378)

* Add workload identity federation support to base-action

Move the workload identity module into base-action so the standalone
action can fetch and refresh the GitHub OIDC identity token itself, and
expose the same federation inputs as the outer action. Switch the
base-action test workflows from the anthropic_api_key secret to the
federation repo variables and grant them id-token: write.

* Verify MCP test tool invocation instead of init connection status

MCP servers can connect asynchronously, so the init event may report a
server as pending. Check that the server is registered at init, then
assert the test tool was actually called and returned its response.
Also pass the MCP config through claude_args --mcp-config, replacing the
removed mcp_config input.

base-action/src/retry.ts

@@ -0,0 +1,47 @@
+export type RetryOptions = {
+  maxAttempts?: number;
+  initialDelayMs?: number;
+  maxDelayMs?: number;
+  backoffFactor?: number;
+  shouldRetry?: (error: Error) => boolean;
+};
+
+export async function retryWithBackoff<T>(
+  operation: () => Promise<T>,
+  options: RetryOptions = {},
+): Promise<T> {
+  const {
+    maxAttempts = 3,
+    initialDelayMs = 5000,
+    maxDelayMs = 20000,
+    backoffFactor = 2,
+    shouldRetry,
+  } = options;
+
+  let delayMs = initialDelayMs;
+  let lastError: Error | undefined;
+
+  for (let attempt = 1; attempt <= maxAttempts; attempt++) {
+    try {
+      console.log(`Attempt ${attempt} of ${maxAttempts}...`);
+      return await operation();
+    } catch (error) {
+      lastError = error instanceof Error ? error : new Error(String(error));
+      console.error(`Attempt ${attempt} failed:`, lastError.message);
+
+      if (shouldRetry && !shouldRetry(lastError)) {
+        console.error("Error is not retryable, giving up immediately");
+        throw lastError;
+      }
+
+      if (attempt < maxAttempts) {
+        console.log(`Retrying in ${delayMs / 1000} seconds...`);
+        await new Promise((resolve) => setTimeout(resolve, delayMs));
+        delayMs = Math.min(delayMs * backoffFactor, maxDelayMs);
+      }
+    }
+  }
+
+  console.error(`Operation failed after ${maxAttempts} attempts`);
+  throw lastError;
+}