feat: add pushBranchForJob helper (src/git/push.ts)

Runs git push -u origin <branch> in the worktree. Detects no-changes
(HEAD = origin/main) before pushing. Classifies push failures into
no-credentials, conflict, or unknown via stderr pattern matching.
5 unit tests covering all paths.

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

src/git/push.ts

@@ -0,0 +1,53 @@
+import { execFile } from 'node:child_process'
+import { promisify } from 'node:util'
+
+const exec = promisify(execFile)
+
+type PushSuccess = { pushed: true; remoteRef: string }
+type PushFailure = {
+  pushed: false
+  reason: 'no-credentials' | 'conflict' | 'no-changes' | 'unknown'
+  stderr: string
+}
+
+export type PushResult = PushSuccess | PushFailure
+
+export async function pushBranchForJob(opts: {
+  worktreePath: string
+  branchName: string
+}): Promise<PushResult> {
+  const { worktreePath, branchName } = opts
+
+  // Detect no new commits vs origin/main
+  let headSha: string
+  let baseSha: string
+  try {
+    const [headResult, baseResult] = await Promise.all([
+      exec('git', ['rev-parse', 'HEAD'], { cwd: worktreePath }),
+      exec('git', ['rev-parse', 'origin/main'], { cwd: worktreePath }),
+    ])
+    headSha = headResult.stdout.trim()
+    baseSha = baseResult.stdout.trim()
+  } catch (err) {
+    return { pushed: false, reason: 'unknown', stderr: (err as Error).message }
+  }
+
+  if (headSha === baseSha) {
+    return { pushed: false, reason: 'no-changes', stderr: '' }
+  }
+
+  // Push
+  try {
+    await exec('git', ['push', '-u', 'origin', branchName], { cwd: worktreePath })
+    return { pushed: true, remoteRef: `refs/heads/${branchName}` }
+  } catch (err) {
+    const stderr = (err as { stderr?: string }).stderr ?? (err as Error).message ?? ''
+    if (/Authentication failed|could not read Username/i.test(stderr)) {
+      return { pushed: false, reason: 'no-credentials', stderr }
+    }
+    if (/non-fast-forward|already exists on the remote|rejected/i.test(stderr)) {
+      return { pushed: false, reason: 'conflict', stderr }
+    }
+    return { pushed: false, reason: 'unknown', stderr }
+  }
+}