fix(split-pane): address Ark0N's fourth pass — PTY-less picker exclusion, hollow chord test, remaining key gates

- buildSplitPickerSessions() now excludes any session with pid === null
  (exited CLI, tripped PTY-exit breaker, a restore that never re-attached).
  Pane B has no equivalent of selectSession()'s auto re-attach POST, so a
  split opened onto one had nothing reading its tmux pane: no terminal
  events ever arrived and Session.write() silently dropped every keystroke
  with no ack either way, while the socket itself reported healthy.
- Fixed the hollow chord regression test: the synthetic keydowns carried no
  keyCode, which is what xterm's evaluateKeyboardEvent switches on to
  produce a data frame at all, so the assertion held regardless of whether
  the gate fired. Adding real keyCodes surfaced a second, real bug in the
  Alt+B case: the event bubbles to app.js's own document-level shortcut
  dispatcher, which really toggles the sidebar and resets the layout
  attribute the gate reads before Pane B's own (later, non-capture) handler
  ever sees it — fixed by driving the app's real settings cache instead of
  only the DOM attribute.
- Ported the two remaining primary-pane gates with real consequences:
  Ctrl+Z (SIGTSTP) is swallowed for every non-shell session, matching
  terminal-ui.js's reasoning (an Ink/TUI agent loop stops dead with no
  visible output otherwise), and Shift/Ctrl+Enter now POSTs to
  /api/sessions/:id/send-key for THIS pane's own session instead of
  letting xterm send a bare \r, which used to submit an incomplete prompt
  instead of inserting a newline. Smart-copy Ctrl+C is re-implemented
  against Pane B's own terminal (copying app.copyTerminalSelection() would
  have copied Pane A's selection instead).
- Updated docs/architecture-invariants.md and docs/split-pane-sessions-plan.md
  to match, and added CLAUDE.md's missing .split-picker-menu z-index entry.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/web/public/constants.js

@@ -1547,6 +1547,14 @@ function buildSplitPickerSessions(sessions, sessionOrder, excludeId, detachedIds
     if (detachedIds?.has?.(id)) continue;
     const session = sessions.get(id);
     if (!session) continue;
+    // A session with no PTY attached (exited CLI, a crash-looped session
+    // whose breaker tripped, a restore that failed to re-attach) has nothing
+    // reading its tmux pane. SplitTerminalPane never does selectSession()'s
+    // re-attach POST, so its socket would open onto a pane nothing feeds:
+    // no terminal events, and Session.write() silently drops every keystroke
+    // with no ack either way (Pane B sends no `seq`), so the loss is
+    // invisible — the healthy socket never trips the disconnect banner.
+    if (session.pid === null) continue;
     result.push({ id, label: session.name || 'Session' });
   }
   return result;