fix(split-pane): stop breaking every settings save, finish the desktop gate

Blocker from Ark0N's second PR #453 pass: moving showSplitButton into
settings-ui.js's per-device displayKeys set was only half of making it
per-device. saveAppSettings() still put it in the object PUT to
/api/settings, SettingsUpdateSchema (.strict()) does not declare it,
the server answered 400 INVALID_INPUT, and because the call site never
checked res.ok the UI still reported "Settings saved" while NOTHING
persisted — workspaceHooksEnabled, agentSkillEnabled, tunnelEnabled,
claudeModel, every toggle, on every save, on every device. Strip it
out via the same destructure every other per-device key goes through
(`showSplitButton: _ssp,`), drop the stray mention from a schemas.ts
comment (a mention there reads as "this is a real field" to the next
grep), and add a static guard test mirroring
test/terminal-auto-copy.test.ts's three-way rule.

Also finishes the desktop gate the first pass only did in CSS at
599px: SPLIT_PANE_MIN_WIDTH (1180, matching HOME_SESSIONS_MIN_WIDTH)
now backs an actual JS width check in _applySplitButtonVisibility,
with a matchMedia listener so a live window resize hides/shows the
button without a reload — the CSS backstop in styles.css is the
reverse-direction guarantee for when JS hasn't run.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/web/public/settings-ui.js

@@ -2352,6 +2352,10 @@ Object.assign(CodemanApp.prototype, {
       showPlanUsageLimits: _pul,
       showAttachmentsButton: _ahb,
       showFileViewerButton: _fvb,
+      // Desktop-only header button, per-device, and absent from
+      // SettingsUpdateSchema (.strict()) — sending it 400s the whole PUT
+      // (moving it into displayKeys alone is not the strip; this is).
+      showSplitButton: _ssp,
       webglRendererEnabled: _wgl,
       terminalWheelLocalScrollback: _twls,
       // Copy-on-select. Per-device (clipboard access differs by device and by
@@ -2950,12 +2954,12 @@ Object.assign(CodemanApp.prototype, {
       multiMonitorBtn.classList.toggle('btn-multimonitor--hidden', !showMultiMonitorButton);
     }
 
-    // Split button — hidden by default
+    // Split button — hidden by default, and hard-gated to desktop widths
+    // regardless of the setting (window.CodemanSplitPane.SPLIT_PANE_MIN_WIDTH,
+    // matching HOME_SESSIONS_MIN_WIDTH's JS-check + media-query-backstop
+    // pattern — the CSS in styles.css is the backstop, this is the check).
     const showSplitButton = settings.showSplitButton ?? defaults.showSplitButton ?? false;
-    const splitBtn = document.querySelector('.btn-split');
-    if (splitBtn) {
-      splitBtn.classList.toggle('btn-split--hidden', !showSplitButton);
-    }
+    this._applySplitButtonVisibility?.(showSplitButton);
 
     // Ultracode/Workflow agents launcher — hidden by default; reveal when enabled.
     // Marker class only (base is display:inline-flex !important) so it's auto-excluded

src/web/schemas.ts

@@ -1376,10 +1376,6 @@ export const SettingsUpdateSchema = z
     showFileBrowser: z.boolean().optional(),
     showSubagents: z.boolean().optional(),
     showMultiMonitorButton: z.boolean().optional(),
-    // showSplitButton is per-device (displayKeys in settings-ui.js) and
-    // deliberately NOT declared here, matching showFileViewerButton/skin/etc:
-    // a desktop opt-in must never sync onto a phone that never asked for it,
-    // and the phone header hard-hides .btn-split regardless (mobile.css).
     // Doubles as the plan-usage telemetry COLLECTION switch, read fresh from
     // disk by readPlanUsageTelemetryEnabled() (hooks-config.ts) at every claude
     // session create/respawn — not just the chip's DISPLAY preference. See that