fix(formation): add working /name-search worker route + e2e harness

Two latent bugs the e2e harness caught:
1. api entities.ts GET /states/:code/name-search calls WORKER_URL/name-search,
   but job_server had NO such route -> 404 -> silently fell back to stale
   entity_cache on every live name check. Added a synchronous /name-search route
   returning {available,exact_match,similar_names,state}.
2. both the new route AND the existing async handle_name_search imported a
   nonexistent search_name_sync(); fixed to drive the real async search_name()
   via an event loop (same pattern as /entity-status).

scripts/e2e-formation-order.mjs: replays the real formation order flow (live
name search -> formation_orders insert -> ERPNext customer + Sales Order with
BUSINESS-FORMATION + STATE-FILING-FEE line items -> verify SO total + DB linkage
-> cleanup) without a real Stripe charge or state filing. Run in the api container.
Also created the missing ERPNext Items (BUSINESS-FORMATION, STATE-FILING-FEE,
FOREIGN-QUAL-SINGLE/MULTI) that the formation SO references.

scripts/workers/job_server.py

@@ -224,7 +224,8 @@ def _check_standard_delay(order_name: str, checkpoint: str) -> dict | None:
 
 def handle_name_search(payload: dict) -> dict:
     """Search for business name availability in a state portal."""
-    from scripts.formation.name_search import search_name_sync
+    import asyncio
+    from scripts.formation.name_search import search_name
     order_name = payload["order_name"]
     state_code = payload["state_code"]
     entity_name = payload["entity_name"]
@@ -235,7 +236,12 @@ def handle_name_search(payload: dict) -> dict:
         return {"action": "name_search", **defer}
 
     LOG.info("Name search: %s in %s", entity_name, state_code)
-    result = search_name_sync(entity_name, state_code)
+    _loop = asyncio.new_event_loop()
+    try:
+        _nsr = _loop.run_until_complete(search_name(entity_name, state_code))
+    finally:
+        _loop.close()
+    result = vars(_nsr) if hasattr(_nsr, "__dict__") else dict(_nsr)
 
     # Report back to ERPNext
     from scripts.workers.erpnext_client import ERPNextClient
@@ -2014,6 +2020,16 @@ class JobHandler(BaseHTTPRequestHandler):
             self._handle_rmd_preview()
             return
 
+        if self.path == "/name-search":
+            # Synchronous name-availability check used by the API
+            # (GET /api/v1/states/:code/name-search). Returns the shape
+            # entities.ts expects: {available, state, exact_match, similar_names}.
+            # This is distinct from /entity-status (which frames the same
+            # search as an entity-status lookup) and from the order-gated
+            # async name_search job (which writes back to ERPNext).
+            self._handle_name_search_sync()
+            return
+
         if self.path == "/jobs/presign":
             # Synchronous presign — used by API routes
             content_length = int(self.headers.get("Content-Length", 0))
@@ -2091,6 +2107,48 @@ class JobHandler(BaseHTTPRequestHandler):
 
         self._respond(202, {"job_id": job_id, "action": action, "status": "queued"})
 
+    def _handle_name_search_sync(self):
+        """Synchronous name-availability check used by the API.
+        POST /name-search {state_code, name}
+        Returns {available, state, exact_match, similar_names} (the shape
+        api/src/routes/entities.ts expects). Calls the live state portal
+        adapter via search_name_sync; the API caches the result for 24h.
+        """
+        content_length = int(self.headers.get("Content-Length", 0))
+        body = self.rfile.read(content_length)
+        try:
+            payload = json.loads(body)
+        except json.JSONDecodeError:
+            self._respond(400, {"error": "Invalid JSON"})
+            return
+
+        state_code = payload.get("state_code", "").strip().upper()
+        name = (payload.get("name") or payload.get("entity_name") or "").strip()
+        if not state_code or not name:
+            self._respond(400, {"error": "state_code and name required"})
+            return
+
+        try:
+            import asyncio
+            from scripts.formation.name_search import search_name
+            loop = asyncio.new_event_loop()
+            result = loop.run_until_complete(search_name(name, state_code))
+            loop.close()
+            if hasattr(result, "__dict__"):
+                result = vars(result)
+            elif hasattr(result, "_asdict"):
+                result = result._asdict()
+            self._respond(200, {
+                "available": result.get("available"),
+                "exact_match": result.get("exact_match"),
+                "similar_names": result.get("similar_names", []),
+                "state": state_code,
+                "source": "live_search",
+            })
+        except Exception as exc:
+            LOG.exception("name-search sync failed for %s/%s", state_code, name)
+            self._respond(500, {"error": str(exc)})
+
     def _handle_entity_status(self):
         """Synchronous entity status lookup via Playwright state adapter.
         POST /entity-status {entity_name, state_code}