feat(desktop): detect and surface gone branches for cleanup

Add `gone` branch detection (upstream tracking ref deleted on remote) to
the composer coding rail and the sidebar project tree, plus a bulk archive
action for sessions on gone branches.

Part 1 — composer "gone" indicator:
- Add `_branch_gone()` to `web_git.py` (remote/REST path) and
  `branchGone()` to `git-review-ops.ts` (Electron local path), both using
  `git for-each-ref --format=%(upstream:track)`.
- Add `gone: boolean` to `HermesRepoStatus` type.
- Show amber "gone" badge in `CodingStatusRow` next to the branch name.
- Rides existing repo-status refresh edges (cwd change, workspace change
  tick, busy→idle, window focus) — no new polling.

Part 2a — session DB staleness fix:
- Re-probe `git_branch`/`git_repo_root` at turn-complete (gateway
  `_run_prompt_submit` finally block) and on session resume (both
  deferred and eager paths), using the existing `_persist_session_git_meta`
  daemon-thread helper. Keeps the session DB's branch column fresh so the
  sidebar tree and gone-branch cleanup are accurate.

Part 2b — sidebar gone-branch detection + cleanup UI:
- Add `gone_branches()` to `git_probe.py` (one `for-each-ref` per repo).
- Add `gone_fn` parameter to `project_tree.build_tree()` + `_annotate_gone()`
  helper that marks branch lanes with `gone: True`.
- Wire `_gone_branches_for_repo` into the gateway's `_build_project_tree`.
- Add `gone?: boolean` to `SidebarSessionGroup` (renderer type).
- Show amber "gone" badge on sidebar branch lanes in `WorkspaceHeader`.
- Add bulk "Archive sessions" action to `WorkspaceMenu` for gone lanes:
  confirms, optimistically tombstones, calls `setSessionArchived` per
  session, surfaces success/failure toasts.
- i18n strings for all 4 locales (en, ja, zh, zh-hant).

Tests:
- `test_status_gone_after_remote_branch_deleted` — E2E with bare remote,
  push, delete, fetch --prune, verify gone=true.
- `test_gone_fn_annotates_branch_lanes` — project tree annotation.
- `test_gone_fn_absent_leaves_no_gone_field` — no spurious gone field.
- Updated `sampleStatus` in coding-status.test.ts with `gone: false`.

tests/hermes_cli/test_web_server_git.py

@@ -54,6 +54,7 @@ def test_status_reports_branch_and_change_counts(client, repo):
     assert body["branch"] == body["defaultBranch"]
     assert body["branch"]
     assert body["detached"] is False
+    assert body["gone"] is False
     # 1 tracked-modified + 1 untracked = 2 changed paths.
     assert body["changed"] == 2
     assert body["untracked"] == 1
@@ -69,6 +70,30 @@ def test_status_returns_null_outside_repo(client, tmp_path):
     assert client.get("/api/git/status", params={"path": str(plain)}).json() is None
 
 
+def test_status_gone_after_remote_branch_deleted(client, repo, tmp_path):
+    """A branch whose upstream was deleted on the remote reports ``gone: true``."""
+    # Set up a bare remote and push a feature branch to it.
+    remote = tmp_path / "remote.git"
+    remote.mkdir()
+    _git(remote, "init", "--bare", "-q")
+    _git(repo, "remote", "add", "origin", str(remote))
+    _git(repo, "checkout", "-q", "-b", "feature/merged")
+    _git(repo, "push", "-q", "-u", "origin", "feature/merged")
+
+    # Branch is live on the remote — not gone.
+    body = client.get("/api/git/status", params={"path": str(repo)}).json()
+    assert body["branch"] == "feature/merged"
+    assert body["gone"] is False
+
+    # Delete the remote branch; `git fetch --prune` updates the tracking ref.
+    _git(repo, "push", "-q", "origin", "--delete", "feature/merged")
+    _git(repo, "fetch", "-q", "--prune", "origin")
+
+    body = client.get("/api/git/status", params={"path": str(repo)}).json()
+    assert body["branch"] == "feature/merged"
+    assert body["gone"] is True
+
+
 def test_review_list_classifies_modified_and_untracked(client, repo):
     body = client.get("/api/git/review/list", params={"path": str(repo)}).json()