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/test/retry.test.ts

@@ -0,0 +1,120 @@
+import { describe, it, expect, beforeEach, afterEach, mock } from "bun:test";
+import { retryWithBackoff } from "../src/retry";
+
+describe("retryWithBackoff", () => {
+  let originalConsoleLog: typeof console.log;
+  let originalConsoleError: typeof console.error;
+
+  beforeEach(() => {
+    originalConsoleLog = console.log;
+    originalConsoleError = console.error;
+    console.log = mock(() => {});
+    console.error = mock(() => {});
+  });
+
+  afterEach(() => {
+    console.log = originalConsoleLog;
+    console.error = originalConsoleError;
+  });
+
+  it("returns the result on first success", async () => {
+    const result = await retryWithBackoff(() => Promise.resolve("ok"), {
+      maxAttempts: 3,
+      initialDelayMs: 1,
+    });
+    expect(result).toBe("ok");
+  });
+
+  it("retries on failure and succeeds", async () => {
+    let attempt = 0;
+    const result = await retryWithBackoff(
+      () => {
+        attempt++;
+        if (attempt < 3) throw new Error("transient");
+        return Promise.resolve("recovered");
+      },
+      { maxAttempts: 3, initialDelayMs: 1 },
+    );
+    expect(result).toBe("recovered");
+    expect(attempt).toBe(3);
+  });
+
+  it("throws after exhausting all attempts", async () => {
+    await expect(
+      retryWithBackoff(() => Promise.reject(new Error("permanent")), {
+        maxAttempts: 2,
+        initialDelayMs: 1,
+      }),
+    ).rejects.toThrow("permanent");
+  });
+
+  it("stops retrying immediately when shouldRetry returns false", async () => {
+    class NonRetryableError extends Error {
+      constructor() {
+        super("non-retryable");
+        this.name = "NonRetryableError";
+      }
+    }
+
+    let attempts = 0;
+    await expect(
+      retryWithBackoff(
+        () => {
+          attempts++;
+          throw new NonRetryableError();
+        },
+        {
+          maxAttempts: 3,
+          initialDelayMs: 1,
+          shouldRetry: (error) => !(error instanceof NonRetryableError),
+        },
+      ),
+    ).rejects.toThrow("non-retryable");
+    expect(attempts).toBe(1);
+  });
+
+  it("continues retrying when shouldRetry returns true", async () => {
+    let attempts = 0;
+    await expect(
+      retryWithBackoff(
+        () => {
+          attempts++;
+          throw new Error("retryable");
+        },
+        {
+          maxAttempts: 3,
+          initialDelayMs: 1,
+          shouldRetry: () => true,
+        },
+      ),
+    ).rejects.toThrow("retryable");
+    expect(attempts).toBe(3);
+  });
+
+  it("preserves the original error when shouldRetry aborts", async () => {
+    class SpecificError extends Error {
+      code = 401;
+      constructor() {
+        super("unauthorized");
+        this.name = "SpecificError";
+      }
+    }
+
+    try {
+      await retryWithBackoff(
+        () => {
+          throw new SpecificError();
+        },
+        {
+          maxAttempts: 3,
+          initialDelayMs: 1,
+          shouldRetry: (error) => !(error instanceof SpecificError),
+        },
+      );
+      expect.unreachable("should have thrown");
+    } catch (error) {
+      expect(error).toBeInstanceOf(SpecificError);
+      expect((error as SpecificError).code).toBe(401);
+    }
+  });
+});