feat(tiles): Tiles header button with a session picker, and a tile's + menu

A Tiles button beside Split in the header, opt-in through the per-device
showTileGridButton setting (read in applyHeaderVisibilitySettings; the
settings checkbox, displayKeys membership and schema exclusion follow with
persistence) and hard-gated like Split: hidden by its --hidden marker, a JS
width check with a live media listener, a @media (max-width: 1179px) backstop
and never in a solo window. While the grid is open the button closes it and
reads as pressed.

Closed, it opens a picker: a checkbox per open session in tab order (never one
popped out to its own window; one with no PTY is offered, its tile shows the
Attach overlay), names as text, preselected with the grid this tab last left,
else the active session and an open split's two. Boxes past what the window
can fit are disabled with the count shown, and Open opens the grid on the
checked sessions, focusing the active one if checked. Escape and an outside
click close it; its close method is idempotent and the global Escape handler
calls it.

A tile's + lists the open sessions not yet tiled; picking one adds it and
focuses it (a human selection). A grid that already holds what the window fits
disables the entries. "New session in this case" waits for auto-join.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

src/web/public/constants.js

@@ -1741,6 +1741,29 @@ function sanitizeTileGridState(raw, liveSessions, detachedIds) {
   };
 }
 
+/**
+ * The sessions the Tiles picker (and a tile's + menu) offers, in tab order:
+ * live ones only, never a session popped out to its own window (that window
+ * owns its PTY size). A session with no PTY attached IS offered: its tile shows
+ * the Attach overlay.
+ *
+ * @param {Map<string, {name?: string}>} sessions
+ * @param {string[]} sessionOrder
+ * @param {{has(id: string): boolean}} [detachedIds]
+ * @param {{has(id: string): boolean}} [exclude] - ids not to offer (already tiled)
+ * @returns {Array<{id: string, label: string}>}
+ */
+function buildTilePickerSessions(sessions, sessionOrder, detachedIds, exclude) {
+  const result = [];
+  for (const id of sessionOrder) {
+    if (detachedIds?.has?.(id) || exclude?.has?.(id)) continue;
+    const session = sessions.get(id);
+    if (!session) continue;
+    result.push({ id, label: session.name || 'Session' });
+  }
+  return result;
+}
+
 /**
  * Which tile takes focus when `id` leaves the grid: the next one in grid
  * order, else the previous one, else null.
@@ -2050,6 +2073,7 @@ if (typeof window !== 'undefined') {
     computeTileLayout,
     tileGridCapacity,
     sanitizeTileGridState,
+    buildTilePickerSessions,
     tileNeighbor,
     tileInDirection,
     cycleTile,