refactor(tiles): the picker's outside-click close loses its left-click leftovers

The Tiles picker opens on right-click now. Three pieces only served the
left-click picker: stopPropagation on the opening event, the tick of delay
before the outside-click listener went in (so the opening click could not
close it), and the exception for clicks on the Tiles button. A right-click
fires no click event, and a left click on the button runs toggleTileGrid,
which closes the picker before the click reaches the document. The
preventDefault that keeps the browser menu away stays.

The outside-click close had no test: tile-grid-open-set now checks that a
click inside the picker leaves it open and one elsewhere closes it.

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

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

@@ -18,7 +18,14 @@ import { readFileSync } from 'node:fs';
 import { resolve } from 'node:path';
 import vm from 'node:vm';
 import { beforeEach, describe, expect, it, vi } from 'vitest';
-import { FakeEl, body, bySelector, makeGridApp, resetGridHarness } from './mocks/tile-grid-vm.js';
+import {
+  FakeEl,
+  body,
+  bySelector,
+  documentAddEventListener,
+  makeGridApp,
+  resetGridHarness,
+} from './mocks/tile-grid-vm.js';
 
 type OpenSet = { source: string; ids: string[]; focusedId: string | null } | null;
 type Helpers = { tileGridOpenSet(p: Record<string, unknown>): OpenSet; TILE_GRID_MAX: number };
@@ -137,6 +144,18 @@ describe('opening at once, in the app', () => {
     expect(app._tilesOwnTerminal()).toBe(true);
   });
 
+  it('a click elsewhere closes the picker; a click inside it does not', () => {
+    const app = makeGridApp(IDS);
+    const before = documentAddEventListener.mock.calls.length;
+    app.openTilePicker({ 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] });
+    expect(picker()).not.toBeNull();
+    onClick({ target: new FakeEl() });
+    expect(picker()).toBeNull();
+  });
+
   it('a right-click opens the picker and keeps the browser menu away', () => {
     const app = makeGridApp(IDS);
     const ev = { preventDefault: vi.fn(), stopPropagation: vi.fn() };