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>

CLAUDE.md

@@ -356,7 +356,7 @@ Frontend JS modules have `@fileoverview` with `@dependency`/`@loadorder` tags. L
 
 **SSE staleness watchdog** (`computeSseStale()` in constants.js, `_checkSseStale()` + a 5s interval in app.js): an `EventSource` that stops delivering does not always error, so `onerror` never fires, the header dot stays green, and every SSE-driven surface (tab status dots, sessions created on another device, renames) freezes until the user reloads. ⚠️ The 15s server keepalive was an SSE **comment** (`:keepalive`), and comments are **invisible to `EventSource` by spec**, so there was nothing a client could observe: it is now the named `sse:heartbeat` event (`cleanupDeadClients()`, sse-stream-manager.ts), which is exactly why the frame had to change type. ⚠️ Staleness is judged **only while the status is `connected`** and the device is online; that guard is the loop breaker, since a forced `connectSSE()` leaves `connected` immediately and cannot re-fire while a reconnect is in flight. ⚠️ The liveness stamp is applied inside `addListener` itself, so every registered handler (the `_SSE_HANDLER_MAP` wrappers AND the directly-registered ones) feeds it from one place; the heartbeat's own listener is a no-op that exists **only** to be registered, since `EventSource` drops named events nobody listens for. ⚠️ The watchdog interval is cleared at the top of `connectSSE()` and nowhere else (its only teardown path); clearing it elsewhere stacks intervals. Recovery needs no new sync path: the reconnect re-runs `handleInit` → `_resetAllAppState()`. The forced reconnect logs one diagnostic line, because a middlebox that strips heartbeats presents as "silently reconnects every 45s".
 
-**Z-index layers**: subagent windows (1000), plan agents (1100), mobile/tablet fixed header (1200, `mobile.css`), modals on ≤768px (1300 — must beat the fixed header or the modal close button is buried), log viewers (2000), connection-loss overlay (2500, above the fixed header and modals), image popups (3000), response viewer (5000, backdrop 4999), file-preview overlay (5100 — must outrank the response viewer, which can launch it; at its old 2000 a path clicked in the chat opened BEHIND the chat), toasts/path picker (10000+, deliberately above the preview), the custom-model center-status banner (10001, `.center-status-banner` — `[hidden]` must re-assert `display: none` over its own `display: flex`, same trap as `.home-sessions[hidden]`, or `dismiss()` leaves an invisible click-blocker dead centre on screen), the swap-confirm and context-warning modals (10010, `#customModelSwapConfirmModal`/`#customModelContextWarningModal` — must clear both the plain `.modal` z-index of 1000 and the center-status banner it can appear over), terminal touch-selection bar (900 — above terminal content and the local-echo overlay, deliberately BELOW floating agent windows so it can never cover their controls), local echo overlay (7).
+**Z-index layers**: subagent windows (1000), split picker menu (1000, `.split-picker-menu`), plan agents (1100), mobile/tablet fixed header (1200, `mobile.css`), modals on ≤768px (1300 — must beat the fixed header or the modal close button is buried), log viewers (2000), connection-loss overlay (2500, above the fixed header and modals), image popups (3000), response viewer (5000, backdrop 4999), file-preview overlay (5100 — must outrank the response viewer, which can launch it; at its old 2000 a path clicked in the chat opened BEHIND the chat), toasts/path picker (10000+, deliberately above the preview), the custom-model center-status banner (10001, `.center-status-banner` — `[hidden]` must re-assert `display: none` over its own `display: flex`, same trap as `.home-sessions[hidden]`, or `dismiss()` leaves an invisible click-blocker dead centre on screen), the swap-confirm and context-warning modals (10010, `#customModelSwapConfirmModal`/`#customModelContextWarningModal` — must clear both the plain `.modal` z-index of 1000 and the center-status banner it can appear over), terminal touch-selection bar (900 — above terminal content and the local-echo overlay, deliberately BELOW floating agent windows so it can never cover their controls), local echo overlay (7).
 
 **Respawn presets**: `solo-work` (3s/60min), `subagent-workflow` (45s/240min), `team-lead` (90s/480min), `ralph-todo` (8s/480min), `overnight-autonomous` (10s/480min).