feat(tiles): right-click Tiles is a 2 / 4 / 6 count menu

Owner decision 10 ("give me then the option to choose only HOW many
tiles, 2,4,6 default is 6 so the menu is easier"; asked where it lives:
"Click opens 6"). The click still opens the grid at once; right-click,
Shift+F10 or the Menu key on the button opens a small menu of three
counts, each drawn as the grid's own layout (2x1, 2x2, 3x2), the
remembered one checked. It replaces the session picker, which is gone
(method, markup hook, CSS, zh-CN entries).

- A pick is remembered per device in codeman:tile-count (default 6;
  codeman:tile-grid stays ids only) and opens that many tiles. The click
  and Ctrl+Shift+G then open with it, at most what the window fits.
- Which sessions: the rule the click already had (the grid this tab
  last had, else an open split's two, else tab order, the active one
  included and focused), trimmed from the end (the focused one kept) or
  filled from tab order to the count. A remembered grid comes back with
  its tiles first, in their cells, holes filled first, then tab order
  (owner answer, superseding decision 8's "exactly the stored set"). A
  page-load restore still brings back exactly what was stored.
- With the grid open a pick re-forms it: a count change is a shape
  change under the cell model's rule (reformTileCells), the focused tile
  always kept, every joining tile mounted and laid out before any of
  them connects, so each fits once and sends one PTY resize.
- Ctrl/Cmd+click on a tab with the grid closed opens the count in total,
  that session among them and focused (owner answer: N, not N+1).
- A count the window cannot fit is greyed out with the reason; a
  remembered one stays checked, the keyboard starts on the largest that
  fits. Arrows, Home/End, Enter or Space; Escape closes the menu alone
  (the global handler gives it the key first, like the tab-group menu)
  and puts the keyboard back on the Tiles button; Tab and a click
  elsewhere close it.
- zh-CN for every new string (N 个窗格, 窗格数量, the titles, the Help
  modal row); the i18n test harvests the menu now, with a session named
  "6 tiles" as the user-text trap.

Tests: tile-grid-picker.test.ts becomes tile-grid-count-menu.test.ts
(the button checks kept, every picker check carried over to the menu,
plus keyboard, remembered count, re-form, Ctrl/Cmd+click and the batch
connect); the open-set, cap, restore, shortcuts, split-coexistence and
i18n expectations follow the count; the Help modal test escapes its
label (the new one has parentheses). The vm harness tracks
document.activeElement and makes SVG elements.

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

src/web/public/index.html

@@ -192,7 +192,7 @@
         <button class="btn-icon-header btn-file-viewer" onclick="app.toggleFileBrowserButton()" title="File Viewer" aria-label="Open file viewer" aria-expanded="false"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M3 7a2 2 0 0 1 2-2h4l2 2h8a2 2 0 0 1 2 2v8a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2z"/></svg></button>
         <button class="btn-icon-header btn-multimonitor btn-multimonitor--hidden" onclick="app.launchMultiMonitor()" title="Open Codeman across all displays" aria-label="Open Codeman across all displays"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="2" y="4" width="13" height="9" rx="1.5"/><rect x="11" y="9" width="11" height="8" rx="1.5"/></svg></button>
         <button class="btn-icon-header btn-split btn-split--hidden" onclick="app.openSplitPicker(event)" title="Split: open a second session beside this one" aria-label="Split: open a second session beside this one" aria-pressed="false"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="2" y="3" width="20" height="18" rx="2"/><line x1="12" y1="3" x2="12" y2="21"/></svg></button>
-        <button class="btn-icon-header btn-tile-grid btn-tile-grid--hidden" onclick="app.toggleTileGrid()" oncontextmenu="app.openTilePicker(event)" title="Tiles: show several sessions side by side (right-click to choose which)" aria-label="Tiles: show several sessions side by side (right-click to choose which)" aria-pressed="false"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="3" y="3" width="8" height="8" rx="1"/><rect x="13" y="3" width="8" height="8" rx="1"/><rect x="3" y="13" width="8" height="8" rx="1"/><rect x="13" y="13" width="8" height="8" rx="1"/></svg></button>
+        <button class="btn-icon-header btn-tile-grid btn-tile-grid--hidden" onclick="app.toggleTileGrid()" oncontextmenu="app.openTileCountMenu(event)" title="Tiles: show several sessions side by side (right-click for how many)" aria-label="Tiles: show several sessions side by side (right-click for how many)" aria-pressed="false"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="3" y="3" width="8" height="8" rx="1"/><rect x="13" y="3" width="8" height="8" rx="1"/><rect x="3" y="13" width="8" height="8" rx="1"/><rect x="13" y="13" width="8" height="8" rx="1"/></svg></button>
         <button class="btn-icon-header btn-ultracode-agents btn-ultracode-agents--hidden" onclick="app.toggleUltracodeAgentsPanel()" title="Ultracode / Workflow agents" aria-label="Open ultracode workflow agents"><svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><circle cx="6" cy="6" r="2.5"/><circle cx="6" cy="18" r="2.5"/><circle cx="18" cy="12" r="2.5"/><path d="M8.2 7.2 15.6 11M8.2 16.8 15.6 13"/></svg></button>
         <div class="header-plan-usage header-plan-usage--hidden" id="planUsageChip" title="Claude and Codex plan usage limits">—</div>
         <button class="btn-icon-header btn-notifications" onclick="app.toggleNotifications()" title="Notifications" aria-label="Toggle notifications" style="display:none;">
@@ -842,7 +842,7 @@
               <div><kbd>Drag</kbd> a tile's header</div><div>Move the Tile (onto Another: Swap)</div>
               <div><kbd>Alt/Option</kbd>+<kbd>Shift</kbd>+<kbd>Enter</kbd></div><div>Zoom Focused Tile</div>
               <div><kbd>Ctrl/Cmd</kbd>+<kbd>Click</kbd> a tab</div><div>Add the Session to the Tile Grid</div>
-              <div><kbd>Right-click</kbd> the Tiles button</div><div>Choose Which Sessions to Tile</div>
+              <div><kbd>Right-click</kbd> the Tiles button</div><div>Choose How Many Tiles (2, 4 or 6)</div>
             </div>
           </section>
           <section class="shortcut-section">