feat(tiles): the per-device Tiles setting, and Ctrl+Shift+G follows it

showTileGridButton gets the full per-device treatment Split has: a header
chip in App Settings beside Split, its load and save lines, OFF by default
(and in the handheld defaults), a member of the displayKeys merge policy,
stripped from the settings PUT and never declared in the .strict()
SettingsUpdateSchema (sending it would 400 the whole save).

The setting also gates the Ctrl+Shift+G toggle (the applied default while the
owner's answer is pending; one line in tileShortcutFor to change): OFF, the
chord is inert and reaches the terminal like any unbound key; ON, it opens and
closes the grid where one can open. A grid that is open however it was opened
(Ctrl/Cmd+click, a dropped tab, "Open group as tiles") keeps all its chords,
the toggle that closes it included.

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

src/web/public/settings-ui.js

@@ -430,6 +430,7 @@ Object.assign(CodemanApp.prototype, {
       settings.ultracodeFloatingWindows ?? defaults.ultracodeFloatingWindows ?? false;
     document.getElementById('appSettingsShowMultiMonitorButton').checked = settings.showMultiMonitorButton ?? defaults.showMultiMonitorButton ?? false;
     document.getElementById('appSettingsShowSplitButton').checked = settings.showSplitButton ?? defaults.showSplitButton ?? false;
+    document.getElementById('appSettingsShowTileGridButton').checked = settings.showTileGridButton ?? defaults.showTileGridButton ?? false;
     document.getElementById('appSettingsShowPlanUsageLimits').checked = this.planUsageChipEnabled(settings);
     document.getElementById('appSettingsShowRedrawButton').checked = settings.showRedrawButton ?? defaults.showRedrawButton ?? false;
     // Phone overview home screen: only meaningful under 600px, so the row is
@@ -2492,6 +2493,7 @@ Object.assign(CodemanApp.prototype, {
       ultracodeFloatingWindows: document.getElementById('appSettingsUltracodeFloatingWindows').checked,
       showMultiMonitorButton: document.getElementById('appSettingsShowMultiMonitorButton').checked,
       showSplitButton: document.getElementById('appSettingsShowSplitButton').checked,
+      showTileGridButton: document.getElementById('appSettingsShowTileGridButton').checked,
       showPlanUsageLimits: document.getElementById('appSettingsShowPlanUsageLimits').checked,
       showRedrawButton: document.getElementById('appSettingsShowRedrawButton').checked,
       mobileOverviewEnabled: document.getElementById('appSettingsMobileOverview').checked,
@@ -2730,6 +2732,9 @@ Object.assign(CodemanApp.prototype, {
       // SettingsUpdateSchema (.strict()) — sending it 400s the whole PUT
       // (moving it into displayKeys alone is not the strip; this is).
       showSplitButton: _ssp,
+      // Same as Split: a per-device header button (and the Tiles chord), absent
+      // from SettingsUpdateSchema (.strict()), so sending it 400s the whole PUT.
+      showTileGridButton: _stg,
       webglRendererEnabled: _wgl,
       terminalWheelLocalScrollback: _twls,
       // Copy-on-select. Per-device (clipboard access differs by device and by
@@ -3420,6 +3425,7 @@ Object.assign(CodemanApp.prototype, {
         ultracodeFloatingWindows: false,
         showMultiMonitorButton: false,
         showSplitButton: false,
+        showTileGridButton: false,
         // Desktop defaults this ON (see planUsageChipEnabled); handhelds keep it
         // OFF so the phone header stays minimal and the mobile-header-buttons
         // policy guard keeps passing.
@@ -4057,6 +4063,7 @@ Object.assign(CodemanApp.prototype, {
           'mobileOverviewEnabled',
           'sessionLineageLines',
           'showSplitButton',
+          'showTileGridButton',
         ]);
         // The plan-usage chip is a PER-DEVICE display setting (desktop default ON,
         // handheld default OFF): desktop can show it while mobile stays hidden. Drop