fix(split-pane): address the rest of Ark0N's PR #453 review

- Exclude popped-out (detached) sessions from the split picker:
  SplitTerminalPane._sendResize() has no yield-to-detached-window check
  the way the primary pane's sendResize() does, so splitting against a
  detached session put its own window and Pane B in a fight over the
  same PTY's dimensions. Simplest fix per the review: keep them out of
  buildSplitPickerSessions() entirely.
- Show a visible dead state when Pane B's WebSocket drops. onData
  already silently discards keystrokes while the socket isn't OPEN
  (there is no reconnect for v1), so a dropped socket left the pane
  looking normal while it quietly ate everything typed into it.
- openSplitPane() returns early with no active session, so a split
  triggered from the home screen no longer creates and connects Pane B
  behind the opaque welcome overlay with nothing to show for it.
- onMove() during a divider drag now bails when the split has
  auto-collapsed mid-drag (the other pane's session ending) instead of
  throwing on `divider.parentElement` being null.
- Promote Pane B via `selectSession(id, { auto: true })` when Pane A's
  session ends — this is an app-driven selection, not the user clicking
  a tab, so it must not spend the promoted session's idle alert.

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

src/web/public/constants.js

@@ -1526,10 +1526,16 @@ function clampDividerPercent(rawPercent, min = 20, max = 80) {
   return rawPercent;
 }
 
-function buildSplitPickerSessions(sessions, sessionOrder, excludeId) {
+function buildSplitPickerSessions(sessions, sessionOrder, excludeId, detachedIds) {
   const result = [];
   for (const id of sessionOrder) {
     if (id === excludeId) continue;
+    // A detached (popped-out) session's own window already yields its PTY
+    // size (see sendResize's detachedElsewhere guard in terminal-ui.js) —
+    // Pane B's SplitTerminalPane._sendResize() has no such check, so letting
+    // one into the picker put its detached window and Pane B in a fight over
+    // the same PTY's dimensions.
+    if (detachedIds?.has?.(id)) continue;
     const session = sessions.get(id);
     if (!session) continue;
     result.push({ id, label: session.name || 'Session' });