perf(offroute): EXISTS guard replaces COUNT(*) on entry_points hot path

The three wilderness-scenario guards used table_exists() OR get_entry_point_count()==0
to check the index is non-empty — a full SELECT COUNT(*) that scanned the entire
2.94M-row table (~9-73s depending on load/cache). Add EntryPointIndex.has_entry_points()
using SELECT EXISTS (SELECT 1 ... LIMIT 1), which short-circuits at the first row, and
swap it into _route_A/_route_B/_route_C. get_entry_point_count() kept for admin-info/tests.

3 new tests: table missing -> False, empty -> False, rows -> True.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/services/navi_offroute/router.py

@@ -197,6 +197,17 @@ class EntryPointIndex:
             cur.execute("SELECT COUNT(*) FROM entry_points")
             return cur.fetchone()[0]
 
+    def has_entry_points(self) -> bool:
+        """Fast non-emptiness check. SELECT EXISTS short-circuits at the first row,
+        unlike SELECT COUNT(*) which scans the entire table (~73s on 2.94M rows).
+        Returns False if the table is absent."""
+        if not self.table_exists():
+            return False
+        conn = self._get_conn()
+        with conn.cursor() as cur:
+            cur.execute("SELECT EXISTS (SELECT 1 FROM entry_points LIMIT 1)")
+            return cur.fetchone()[0]
+
     def query_bbox(
         self,
         south: float,
@@ -905,7 +916,7 @@ class OffrouteRouter:
         t0 = time.time()
 
         # Ensure entry point index exists
-        if not self.entry_index.table_exists() or self.entry_index.get_entry_point_count() == 0:
+        if not self.entry_index.has_entry_points():
             return {
                 "status": "error",
                 "message": "Trail entry point index not built. Run build_entry_index() first."
@@ -986,7 +997,7 @@ class OffrouteRouter:
         """
         t0 = time.time()
 
-        if not self.entry_index.table_exists() or self.entry_index.get_entry_point_count() == 0:
+        if not self.entry_index.has_entry_points():
             return {
                 "status": "error",
                 "message": "Trail entry point index not built. Run build_entry_index() first."
@@ -1066,7 +1077,7 @@ class OffrouteRouter:
         """
         t0 = time.time()
 
-        if not self.entry_index.table_exists() or self.entry_index.get_entry_point_count() == 0:
+        if not self.entry_index.has_entry_points():
             return {
                 "status": "error",
                 "message": "Trail entry point index not built. Run build_entry_index() first."

backend/services/navi_offroute/tests/test_offroute.py

@@ -465,3 +465,50 @@ def test_spatial_no_class_no_use_picks_foot(monkeypatch):
     r = object.__new__(OffrouteRouter)
     modes = r._spatial_eligible_modes(43.6, -116.2, {})
     assert modes == frozenset({"foot"})
+
+
+# ── EntryPointIndex.has_entry_points — EXISTS guard (replaces COUNT(*)) ────
+# Bare index (no __init__/DB); table_exists + _get_conn monkeypatched.
+
+from services.navi_offroute.router import EntryPointIndex
+
+
+class _FakeCur:
+    def __init__(self, row):
+        self._row = row
+    def __enter__(self):
+        return self
+    def __exit__(self, *a):
+        return False
+    def execute(self, q, *a):
+        self.q = q
+    def fetchone(self):
+        return self._row
+
+
+class _FakeConn:
+    def __init__(self, row):
+        self._row = row
+    def cursor(self):
+        return _FakeCur(self._row)
+
+
+def _bare_index(monkeypatch, table_exists, row=None):
+    monkeypatch.setattr(EntryPointIndex, "table_exists", lambda self: table_exists)
+    monkeypatch.setattr(EntryPointIndex, "_get_conn", lambda self: _FakeConn(row))
+    return object.__new__(EntryPointIndex)
+
+
+def test_has_entry_points_table_missing(monkeypatch):
+    idx = _bare_index(monkeypatch, table_exists=False)
+    assert idx.has_entry_points() is False
+
+
+def test_has_entry_points_empty(monkeypatch):
+    idx = _bare_index(monkeypatch, table_exists=True, row=(False,))
+    assert idx.has_entry_points() is False
+
+
+def test_has_entry_points_rows(monkeypatch):
+    idx = _bare_index(monkeypatch, table_exists=True, row=(True,))
+    assert idx.has_entry_points() is True