fix(state): keep /branch sessions visible after parent reopen

/branch (aka /fork) sessions vanished from /resume and /sessions. Both
surfaces funnel through list_sessions_rich(include_children=False), which
hid any session with a parent_session_id unless identified as a branch via a
heuristic — parent.end_reason == 'branched' AND child.started_at >=
parent.ended_at.

Two ways that heuristic failed:
1. CLI/gateway branches: once the parent was reopened (e.g. resumed) and
   re-ended with a different end_reason (tui_shutdown overwriting 'branched'),
   the heuristic stopped matching and the branch was hidden permanently.
2. TUI branches (tui_gateway session.branch): the TUI never ends the parent
   as 'branched' — it creates the child while the parent is still live — so
   the heuristic NEVER matched and TUI branches were hidden from the moment
   they were created (this is the macOS desktop app's primary symptom).

Fix: persist a stable '_branched_from' marker in the branch session's
model_config at creation time across ALL THREE branch paths (CLI cli.py,
gateway gateway/run.py, and TUI tui_gateway/server.py), and OR a
json_extract(model_config, '$._branched_from') IS NOT NULL check into the
list_sessions_rich filter. The marker is immutable across the parent's
lifecycle, so the branch stays visible regardless of how/whether the parent
is ended. The legacy end_reason heuristic is kept (OR'd) so pre-existing
branches remain visible. Subagent/compression children (no marker, parent
not 'branched') stay correctly hidden. Fixes #20856.

Approach by liuhao1024 (PR #20864); reimplemented on current main, extended
to the TUI branch path (which the original missed), with regression tests for
the reopen+re-end scenario and the TUI marker persistence.

tests/tui_gateway/test_protocol.py

@@ -613,6 +613,71 @@ def test_session_resume_live_payload_uses_current_history_with_ancestors(server,
     ]
 
 
+def test_session_branch_persists_branched_from_marker(server, monkeypatch):
+    """TUI /branch must persist a _branched_from marker so the branch stays
+    visible in /resume and /sessions.
+
+    Regression for issue #20856: the TUI branch leaves the parent live (it
+    never ends it with end_reason='branched'), so list_sessions_rich's legacy
+    heuristic never surfaces it — the stable model_config marker is the only
+    thing that keeps a TUI branch visible.
+    """
+    create_calls = []
+
+    class _DB:
+        def get_session_title(self, _key):
+            return "parent-title"
+
+        def get_next_title_in_lineage(self, base):
+            return f"{base} 2"
+
+        def create_session(self, new_key, **kwargs):
+            create_calls.append((new_key, kwargs))
+            return new_key
+
+        def append_message(self, **_kwargs):
+            return None
+
+        def set_session_title(self, _key, _title):
+            return None
+
+    monkeypatch.setattr(server, "_get_db", lambda: _DB())
+    monkeypatch.setattr(server, "_resolve_model", lambda: "test/model")
+    monkeypatch.setattr(server, "_new_session_key", lambda: "20260101_000001_child0")
+    monkeypatch.setattr(
+        server,
+        "_make_agent",
+        lambda _sid, key, session_id=None: types.SimpleNamespace(
+            model="test/model", session_id=session_id or key
+        ),
+    )
+    monkeypatch.setattr(server, "_init_session", lambda *_a, **_k: None)
+    monkeypatch.setattr(server, "_set_session_context", lambda *_a, **_k: [])
+    monkeypatch.setattr(server, "_clear_session_context", lambda *_a, **_k: None)
+    monkeypatch.setattr(server, "_session_cwd", lambda _s: "/tmp/branch-cwd")
+
+    parent_sid = "parent01"
+    parent_key = "20260101_000000_parent"
+    server._sessions[parent_sid] = {
+        "session_key": parent_key,
+        "history": [{"role": "user", "content": "hello"}],
+        "history_lock": threading.Lock(),
+        "cols": 80,
+    }
+
+    resp = server.handle_request(
+        {"id": "b1", "method": "session.branch", "params": {"session_id": parent_sid}}
+    )
+
+    assert "error" not in resp, resp
+    assert len(create_calls) == 1
+    new_key, kwargs = create_calls[0]
+    assert new_key == "20260101_000001_child0"
+    assert kwargs["parent_session_id"] == parent_key
+    # The marker — without it the branch is invisible in /resume and /sessions.
+    assert kwargs["model_config"] == {"_branched_from": parent_key}
+
+
 def test_make_agent_accepts_list_system_prompt(server, monkeypatch):
     captured = {}