feat: add push event support for automation workflows

Add support for `push` events as an automation event type, enabling
workflows triggered by pushes to use claude-code-action.

Changes:
- Add PushEvent to automation event types in context.ts
- Add case handler for push events in parseGitHubContext()
- Add isPushEvent() type guard
- Add test for push event mode detection

This enables use cases like auto-rebasing PRs when main is updated,
where a workflow triggers on push to main and uses a prompt to
instruct Claude to merge main into stale PR branches.

src/github/context.ts

@@ -6,6 +6,7 @@ import type {
   PullRequestEvent,
   PullRequestReviewEvent,
   PullRequestReviewCommentEvent,
+  PushEvent,
   WorkflowRunEvent,
 } from "@octokit/webhooks-types";
 import { CLAUDE_APP_BOT_ID, CLAUDE_BOT_LOGIN } from "./constants";
@@ -65,6 +66,7 @@ const AUTOMATION_EVENT_NAMES = [
   "repository_dispatch",
   "schedule",
   "workflow_run",
+  "push",
 ] as const;
 
 // Derive types from constants for better maintainability
@@ -112,14 +114,15 @@ export type ParsedGitHubContext = BaseContext & {
   isPR: boolean;
 };
 
-// Context for automation events (workflow_dispatch, repository_dispatch, schedule, workflow_run)
+// Context for automation events (workflow_dispatch, repository_dispatch, schedule, workflow_run, push)
 export type AutomationContext = BaseContext & {
   eventName: AutomationEventName;
   payload:
     | WorkflowDispatchEvent
     | RepositoryDispatchEvent
     | ScheduleEvent
-    | WorkflowRunEvent;
+    | WorkflowRunEvent
+    | PushEvent;
 };
 
 // Union type for all contexts
@@ -235,6 +238,13 @@ export function parseGitHubContext(): GitHubContext {
         payload: context.payload as unknown as WorkflowRunEvent,
       };
     }
+    case "push": {
+      return {
+        ...commonFields,
+        eventName: "push",
+        payload: context.payload as unknown as PushEvent,
+      };
+    }
     default:
       throw new Error(`Unsupported event type: ${context.eventName}`);
   }
@@ -276,6 +286,12 @@ export function isIssuesAssignedEvent(
   return isIssuesEvent(context) && context.eventAction === "assigned";
 }
 
+export function isPushEvent(
+  context: GitHubContext,
+): context is AutomationContext & { payload: PushEvent } {
+  return context.eventName === "push";
+}
+
 // Type guard to check if context is an entity context (has entityNumber and isPR)
 export function isEntityContext(
   context: GitHubContext,

test/modes/registry.test.ts

@@ -60,6 +60,15 @@ describe("Mode Registry", () => {
     expect(mode.name).toBe("agent");
   });
 
+  test("getMode auto-detects agent for push event", () => {
+    const pushContext = createMockAutomationContext({
+      eventName: "push",
+    });
+    const mode = getMode(pushContext);
+    expect(mode).toBe(agentMode);
+    expect(mode.name).toBe("agent");
+  });
+
   test("getMode auto-detects agent for repository_dispatch with client_payload", () => {
     const contextWithPayload = createMockAutomationContext({
       eventName: "repository_dispatch",