feat: integrate push into update_job_status DONE transition

On status=done, calls pushBranchForJob before DB write:
- pushed=true → DONE + pushed_at + branch set + worktree cleanup (keepBranch=true)
- no-changes → DONE without pushed_at + worktree cleanup
- push failure → FAILED with error message + worktree preserved for manual inspection

Also adds pushed_at to vendored prisma schema + regenerates client.
6 unit tests for prepareDoneUpdate covering all push outcomes.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

__tests__/update-job-status-push.test.ts

@@ -0,0 +1,110 @@
+import { describe, it, expect, vi, beforeEach, afterEach } from 'vitest'
+import * as path from 'node:path'
+
+vi.mock('../src/git/push.js', () => ({
+  pushBranchForJob: vi.fn(),
+}))
+
+import { pushBranchForJob } from '../src/git/push.js'
+import { prepareDoneUpdate } from '../src/tools/update-job-status.js'
+
+const mockPush = pushBranchForJob as ReturnType<typeof vi.fn>
+
+beforeEach(() => {
+  vi.clearAllMocks()
+})
+
+describe('prepareDoneUpdate', () => {
+  const originalEnv = { ...process.env }
+
+  afterEach(() => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = originalEnv.SCRUM4ME_AGENT_WORKTREE_DIR
+  })
+
+  it('returns DONE with pushedAt and branchOverride when push succeeds', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({ pushed: true, remoteRef: 'refs/heads/feat/job-abc' })
+
+    const plan = await prepareDoneUpdate('job-abc', 'feat/job-abc')
+
+    expect(plan.dbStatus).toBe('DONE')
+    expect(plan.pushedAt).toBeInstanceOf(Date)
+    expect(plan.branchOverride).toBe('feat/job-abc')
+    expect(plan.errorOverride).toBeUndefined()
+    expect(plan.skipWorktreeCleanup).toBe(false)
+
+    expect(mockPush).toHaveBeenCalledWith({
+      worktreePath: path.join('/wt', 'job-abc'),
+      branchName: 'feat/job-abc',
+    })
+  })
+
+  it('derives branchName from jobId when branch is undefined', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({ pushed: true, remoteRef: 'refs/heads/feat/job-abc12345' })
+
+    await prepareDoneUpdate('job-abc12345', undefined)
+
+    expect(mockPush).toHaveBeenCalledWith(
+      expect.objectContaining({ branchName: 'feat/job-abc12345' }),
+    )
+  })
+
+  it('returns DONE without pushedAt when no-changes', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({ pushed: false, reason: 'no-changes', stderr: '' })
+
+    const plan = await prepareDoneUpdate('job-abc', 'feat/job-abc')
+
+    expect(plan.dbStatus).toBe('DONE')
+    expect(plan.pushedAt).toBeUndefined()
+    expect(plan.branchOverride).toBeUndefined()
+    expect(plan.errorOverride).toBeUndefined()
+    expect(plan.skipWorktreeCleanup).toBe(false)
+  })
+
+  it('returns FAILED with error and skipWorktreeCleanup when no-credentials', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({
+      pushed: false,
+      reason: 'no-credentials',
+      stderr: 'fatal: Authentication failed',
+    })
+
+    const plan = await prepareDoneUpdate('job-abc', 'feat/job-abc')
+
+    expect(plan.dbStatus).toBe('FAILED')
+    expect(plan.errorOverride).toContain('push failed (no-credentials)')
+    expect(plan.errorOverride).toContain('Authentication failed')
+    expect(plan.skipWorktreeCleanup).toBe(true)
+  })
+
+  it('returns FAILED with error and skipWorktreeCleanup when conflict', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({
+      pushed: false,
+      reason: 'conflict',
+      stderr: '! [rejected] non-fast-forward',
+    })
+
+    const plan = await prepareDoneUpdate('job-abc', 'feat/job-abc')
+
+    expect(plan.dbStatus).toBe('FAILED')
+    expect(plan.errorOverride).toContain('push failed (conflict)')
+    expect(plan.skipWorktreeCleanup).toBe(true)
+  })
+
+  it('returns FAILED with error and skipWorktreeCleanup when unknown push error', async () => {
+    process.env.SCRUM4ME_AGENT_WORKTREE_DIR = '/wt'
+    mockPush.mockResolvedValue({
+      pushed: false,
+      reason: 'unknown',
+      stderr: 'something went wrong',
+    })
+
+    const plan = await prepareDoneUpdate('job-abc', 'feat/job-abc')
+
+    expect(plan.dbStatus).toBe('FAILED')
+    expect(plan.skipWorktreeCleanup).toBe(true)
+  })
+})