Persist home stepper state to localStorage via freeze scope

- freeze-scope "home-stepper" captures step-idx signal
- Each step/back saves to localStorage via freeze-to-sx
- On mount, restores from localStorage via thaw-from-sx
- Invalid state resets to default (step 9)
- Clear preview lake before replay to prevent duplicates
- Register local-storage-get/set/remove as primitives
- Arrows 3x bigger

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

shared/sx/ref/platform_js.py

@@ -2912,6 +2912,9 @@ PLATFORM_BOOT_JS = """
   function localStorageRemove(key) {
     try { localStorage.removeItem(key); } catch (e) {}
   }
+  PRIMITIVES["local-storage-get"] = localStorageGet;
+  PRIMITIVES["local-storage-set"] = localStorageSet;
+  PRIMITIVES["local-storage-remove"] = localStorageRemove;
 
   // --- Cookies ---