Refactor and optimize: deduplicate, batch queries, fix bugs

- Remove unused DATABASE_PATH import from games.py
- Extract _new_game_context(db) helper to deduplicate GET/POST error path
- Extract _parse_hole_form() helper to deduplicate hole validation in create/edit course
- Batch N+1 player handicap and tee queries in create_game into two IN() queries
- Fix hole count import bug: use max() across all tees instead of first match
- Fix migration exception handling: re-raise unless "duplicate column name"
- Cache calcSkins() result in _skinsCache; invalidate on score/skip changes
- Collapse two identical Next buttons into one in new_game.html
- Fix stale skinDoubleBackNine checkbox: reset on mode change, use x-model

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/routers/courses.py

@@ -51,6 +51,36 @@ async def _get_course_detail(cid: str, db: aiosqlite.Connection):
     return dict(course), holes, tees
 
 
+def _parse_hole_form(form, hole_count: int) -> tuple[dict, dict, dict]:
+    """Parse par/SI fields from a form. Returns (pars, stroke_indices, errors)."""
+    pars: dict[int, int] = {}
+    stroke_indices: dict[int, int | None] = {}
+    errors: dict[str, str] = {}
+    for i in range(1, hole_count + 1):
+        raw = form.get(f"par_{i}", "4")
+        try:
+            p = int(raw)
+            if p < 3 or p > 5:
+                errors[f"par_{i}"] = f"Hole {i}: par must be 3–5."
+            else:
+                pars[i] = p
+        except (ValueError, TypeError):
+            errors[f"par_{i}"] = f"Hole {i}: invalid par."
+        raw_si = form.get(f"si_{i}", "")
+        if raw_si:
+            try:
+                si = int(raw_si)
+                if si < 1 or si > hole_count:
+                    errors[f"si_{i}"] = f"Hole {i}: SI must be 1–{hole_count}."
+                else:
+                    stroke_indices[i] = si
+            except (ValueError, TypeError):
+                errors[f"si_{i}"] = f"Hole {i}: invalid SI."
+        else:
+            stroke_indices[i] = None
+    return pars, stroke_indices, errors
+
+
 # ── List ──────────────────────────────────────────────────────────────────────
 
 @router.get("/admin/courses", response_class=HTMLResponse)
@@ -91,30 +121,8 @@ async def create_course(request: Request,
         errors["holes"] = "Holes must be 9 or 18."
 
     hole_count = holes if holes in (9, 18) else 18
-    pars = {}
-    stroke_indices = {}
-    for i in range(1, hole_count + 1):
-        raw = form.get(f"par_{i}", "4")
-        try:
-            p = int(raw)
-            if p < 3 or p > 5:
-                errors[f"par_{i}"] = f"Hole {i}: par must be 3–5."
-            else:
-                pars[i] = p
-        except (ValueError, TypeError):
-            errors[f"par_{i}"] = f"Hole {i}: invalid par."
-        raw_si = form.get(f"si_{i}", "")
-        if raw_si:
-            try:
-                si = int(raw_si)
-                if si < 1 or si > hole_count:
-                    errors[f"si_{i}"] = f"Hole {i}: SI must be 1–{hole_count}."
-                else:
-                    stroke_indices[i] = si
-            except (ValueError, TypeError):
-                errors[f"si_{i}"] = f"Hole {i}: invalid SI."
-        else:
-            stroke_indices[i] = None
+    pars, stroke_indices, hole_errors = _parse_hole_form(form, hole_count)
+    errors.update(hole_errors)
 
     if errors:
         return templates.TemplateResponse(
@@ -187,16 +195,12 @@ async def import_course(api_id: int, request: Request,
     else:
         location = (loc.get("address") or "").strip()
 
-    # Determine hole count from tees
+    # Determine hole count from tees — use max so a course with any 18-hole tee stays 18
     tees_male = data.get("tees", {}).get("male") or []
     tees_female = data.get("tees", {}).get("female") or []
     all_tees = tees_male + tees_female
-    holes_count = 18
-    for t in all_tees:
-        n = t.get("number_of_holes")
-        if n in (9, 18):
-            holes_count = n
-            break
+    valid_counts = [t.get("number_of_holes") for t in all_tees if t.get("number_of_holes") in (9, 18)]
+    holes_count = max(valid_counts, default=18)
 
     # Hole par + course-level stroke index from first male tee with hole data (fallback for display)
     hole_pars: dict[int, int] = {}
@@ -286,30 +290,8 @@ async def edit_course_submit(cid: str, request: Request,
         errors["holes"] = "Holes must be 9 or 18."
 
     hole_count = holes if holes in (9, 18) else 18
-    pars = {}
-    stroke_indices = {}
-    for i in range(1, hole_count + 1):
-        raw = form.get(f"par_{i}", "4")
-        try:
-            p = int(raw)
-            if p < 3 or p > 5:
-                errors[f"par_{i}"] = f"Hole {i}: par must be 3–5."
-            else:
-                pars[i] = p
-        except (ValueError, TypeError):
-            errors[f"par_{i}"] = f"Hole {i}: invalid par."
-        raw_si = form.get(f"si_{i}", "")
-        if raw_si:
-            try:
-                si = int(raw_si)
-                if si < 1 or si > hole_count:
-                    errors[f"si_{i}"] = f"Hole {i}: SI must be 1–{hole_count}."
-                else:
-                    stroke_indices[i] = si
-            except (ValueError, TypeError):
-                errors[f"si_{i}"] = f"Hole {i}: invalid SI."
-        else:
-            stroke_indices[i] = None
+    pars, stroke_indices, hole_errors = _parse_hole_form(form, hole_count)
+    errors.update(hole_errors)
 
     if errors:
         return templates.TemplateResponse(