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>

test/tile-grid-open-set.test.ts

@@ -8,8 +8,8 @@
  *   focused. Detached sessions and ones that no longer exist are left out, as
  *   in the picker.
  * - The button's click and Ctrl+Shift+G are the same function
- *   (`toggleTileGrid`); right-click (contextmenu) opens the picker. With the
- *   grid open the picker shows the current tiles, and Open replaces them.
+ *   (`toggleTileGrid`); right-click (contextmenu) opens the count menu (owner
+ *   decision 10). With the grid open a pick re-forms it, the focused tile kept.
  *
  * The pure helper and the app both via the shared harness (test/mocks/tile-grid-vm.ts).
  * Port: N/A.
@@ -99,11 +99,11 @@ describe('the Tiles button and Ctrl+Shift+G', () => {
     return html;
   };
 
-  it('a click opens the grid at once (the toggle), a right-click opens the picker', () => {
+  it('a click opens the grid at once (the toggle), a right-click opens the count menu', () => {
     expect(button()).toContain('onclick="app.toggleTileGrid()"');
-    expect(button()).toContain('oncontextmenu="app.openTilePicker(event)"');
-    expect(button()).toContain('right-click to choose which');
-    expect(button()).not.toContain('onclick="app.openTilePicker');
+    expect(button()).toContain('oncontextmenu="app.openTileCountMenu(event)"');
+    expect(button()).toContain('right-click for how many');
+    expect(button()).not.toContain('onclick="app.openTileCountMenu');
   });
 
   it('Ctrl+Shift+G runs the same toggle', () => {
@@ -114,14 +114,18 @@ describe('the Tiles button and Ctrl+Shift+G', () => {
 
 describe('opening at once, in the app', () => {
   const IDS = ['s-a', 's-b', 's-c'];
-  const picker = () => body.children.find((c) => c.id === 'tilePickerMenu') ?? null;
+  const picker = () => body.children.find((c) => c.id === 'tileCountMenu') ?? null;
+  const pick = (n: number) =>
+    picker()!
+      .children.find((c) => c.dataset.count === String(n))!
+      .dispatch('click', { stopPropagation: vi.fn() });
   beforeEach(() => {
     resetGridHarness();
     const wrap = new FakeEl();
     bySelector.set('.terminal-wrap', wrap);
   });
 
-  it('a click with the grid closed shows the tiles, no picker', () => {
+  it('a click with the grid closed shows the tiles, no menu', () => {
     const app = makeGridApp(IDS);
     app.activeSessionId = 's-b';
     app.toggleTileGrid();
@@ -131,19 +135,19 @@ describe('opening at once, in the app', () => {
     expect(app.activeSessionId).toBe('s-b');
   });
 
-  it('a click closes a picker that a right-click left open', () => {
+  it('a click closes a menu that a right-click left open', () => {
     const app = makeGridApp(IDS);
-    app.openTilePicker({ preventDefault: vi.fn(), stopPropagation: vi.fn() });
+    app.openTileCountMenu({ preventDefault: vi.fn(), stopPropagation: vi.fn() });
     expect(picker()).not.toBeNull();
     app.toggleTileGrid();
     expect(picker()).toBeNull();
     expect(app._tilesOwnTerminal()).toBe(true);
   });
 
-  it('a click elsewhere closes the picker; a click inside it does not', () => {
+  it('a click elsewhere closes the menu; a click inside it does not', () => {
     const app = makeGridApp(IDS);
     const before = documentAddEventListener.mock.calls.length;
-    app.openTilePicker({ preventDefault: vi.fn() });
+    app.openTileCountMenu({ preventDefault: vi.fn() });
     const calls = documentAddEventListener.mock.calls.slice(before) as Array<[string, (e: unknown) => void]>;
     const onClick = calls.find(([type]) => type === 'click')![1];
     onClick({ target: picker()!.children[0] });
@@ -152,31 +156,27 @@ describe('opening at once, in the app', () => {
     expect(picker()).toBeNull();
   });
 
-  it('a right-click opens the picker and keeps the browser menu away', () => {
+  it('a right-click opens the count menu and keeps the browser menu away', () => {
     const app = makeGridApp(IDS);
     const ev = { preventDefault: vi.fn(), stopPropagation: vi.fn() };
-    app.openTilePicker(ev);
+    app.openTileCountMenu(ev);
     expect(ev.preventDefault).toHaveBeenCalled();
     expect(picker()).not.toBeNull();
     expect(app._tilesOwnTerminal()).toBe(false);
   });
 
-  it('a right-click with the grid open shows its tiles; Open replaces them', () => {
+  it('a right-click with the grid open re-forms it to the count picked, the focused tile kept', () => {
     const app = makeGridApp(IDS);
     app.openTileGrid(['s-a', 's-b'], { focusedId: 's-b' });
-    app.openTilePicker({ preventDefault: vi.fn(), stopPropagation: vi.fn() });
+    app.openTileCountMenu({ preventDefault: vi.fn(), stopPropagation: vi.fn() });
     expect(app._tilesOwnTerminal()).toBe(true);
-    const menu = picker()!;
-    const boxes = menu.children[0].children.map((row) => row.children[0]);
-    expect(boxes.filter((b) => b.checked).map((b) => b.value)).toEqual(['s-a', 's-b']);
-    const boxA = boxes.find((b) => b.value === 's-a')!;
-    boxA.checked = false;
-    boxA.dispatch('change');
-    const boxC = boxes.find((b) => b.value === 's-c')!;
-    boxC.checked = true;
-    boxC.dispatch('change');
-    menu.children[1].children[1].dispatch('click');
-    expect(app._tileGrid.ids).toEqual(['s-b', 's-c']);
+    pick(4);
+    // Its two first, then the open sessions in tab order.
+    expect(app._tileGrid.ids).toEqual(['s-a', 's-b', 's-other', 's-c']);
+    expect(app.activeSessionId).toBe('s-b');
+    app.openTileCountMenu({ preventDefault: vi.fn(), stopPropagation: vi.fn() });
+    pick(2);
+    expect(app._tileGrid.ids).toEqual(['s-a', 's-b']);
     expect(app.activeSessionId).toBe('s-b');
   });
 });