fix(terminal): unsubscribe when the SSE header write fails after attaching

Adversarial review of the previous commit found a leak it introduced.

`attach_terminal()` subscribes and only then are the response headers written.
A client that dropped in that instant makes `end_headers()` raise
BrokenPipeError/ConnectionResetError, and because the `try/finally` started
*after* those writes, the exception escaped `_handle_terminal_output` with the
queue still in `_subscribers`. That pins `unwatched_since` at None — only
`unsubscribe()` on an empty subscriber list resets it — so the terminal became
permanently unreapable: the exact fd/thread leak (#4633) this reaper exists to
prevent, and strictly worse than the TOCTOU the previous commit fixed, since
that at least still allowed cleanup.

The try now starts immediately after the attach, so every exit path
unsubscribes. Regression test drives a handler whose `end_headers()` raises and
asserts the subscriber list is empty, `unwatched_since` is restored, and the
terminal is reapable again once the grace elapses. It fails against the
previous ordering.

tests/test_terminal_idle_reaper.py

@@ -340,3 +340,53 @@ def test_teardown_runs_without_holding_the_registry_lock(monkeypatch):
     terminal._reap_idle_terminals(time.time())
 
     assert observed.get("free") is True, "_LOCK was held across process teardown"
+
+
+def test_a_header_write_failure_after_attach_still_unsubscribes(monkeypatch):
+    """Attaching before the headers must not be able to leak the subscriber.
+
+    `attach_terminal()` subscribes, and only then are the response headers
+    written. A client that dropped in that instant makes `end_headers()` raise
+    BrokenPipeError; if that escaped before the try/finally, the queue would
+    stay in `_subscribers` forever, pin `unwatched_since` at None, and make the
+    terminal permanently unreapable — the very leak this reaper exists to
+    prevent, self-inflicted.
+    """
+    import io
+    from types import SimpleNamespace
+
+    import api.routes as routes
+
+    sid = "sse-header-failure"
+    term = _make_registered_term(monkeypatch, sid, unwatched_since=_expired_since())
+
+    class _Handler:
+        headers = {}
+
+        def __init__(self):
+            self.wfile = io.BytesIO()
+            self.status = None
+
+        def send_response(self, status):
+            self.status = status
+
+        def send_header(self, _name, _value):
+            pass
+
+        def end_headers(self):
+            raise ConnectionResetError("client vanished")
+
+    monkeypatch.setattr(routes, "_embedded_terminal_gate_allows", lambda _handler: True)
+    monkeypatch.setattr(routes, "_sse_set_write_deadline", lambda _handler: None)
+
+    routes._handle_terminal_output(
+        _Handler(), SimpleNamespace(query=f"session_id={sid}")
+    )
+
+    assert term._subscribers == [], "the subscriber leaked on a header-write failure"
+    assert term.unwatched_since is not None, "the terminal was pinned as watched forever"
+    # The grace restarts from the detach, which is correct — but the terminal
+    # is reapable again once it elapses, instead of being pinned forever.
+    assert terminal._reap_idle_terminals(
+        term.unwatched_since + terminal._TERMINAL_IDLE_GRACE_SECONDS + 1
+    ) == 1