feat(catalog): part-count signposting + drill hint for deep category trees

pcat/emex vehicles decode into a tree whose top level is ~100% folders with
zero parts (6746/9458 root nodes are parents, 0 direct leaves across 477
vehicles). Users — serkan filazi among them — saw an opaque wall of identical
folder cards, assumed the parts feature was missing, and bounced without ever
drilling (his session: 3 view-mode toggles, 0 category clicks; his data was
2-3 clicks deep and fully reachable).

Two changes, no upstream/proxy cost:
- getCategoryTree now rolls up a subtree partCount per node (one grouped parts
  read + JS post-order sum). The grid already renders "N parça", so folders
  now read "Fren sistemi · 142 parça" and steer drilling toward the branches
  that actually contain parts; empty branches stay quiet. Counts reflect
  drilled data and grow as branches are visited.
- A one-line drill hint on a "cold" tree (nothing drilled yet → no counts) so
  first-visit users know parts live inside the subcategories instead of reading
  the folder wall as a broken/empty catalog. Drops away once any branch is hit.

Verified: subtree roll-up unit test + existing suite (10/10), tsc + biome clean
across api/web/shared.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

apps/web/src/routes/dashboard/vehicles_/$id/index.tsx

@@ -26,7 +26,7 @@ import { Skeleton } from "@sase/ui";
 import { Button } from "@sase/ui";
 import { useQuery } from "@tanstack/react-query";
 import { createFileRoute, useCanGoBack, useNavigate, useRouter } from "@tanstack/react-router";
-import { ArrowLeft } from "lucide-react";
+import { ArrowLeft, Info } from "lucide-react";
 import { useEffect, useState } from "react";
 
 import { KEYS_8 } from "@/lib/keys";
@@ -92,6 +92,15 @@ function VehicleDetailPage() {
     enabled: !!id && idValid,
   });
 
+  // A "cold" tree has nothing drilled yet — no part counts anywhere. This is the
+  // normal first-visit state for pcat/emex vehicles, whose top level is entirely
+  // folders with zero parts. Without a nudge users read that folder wall as
+  // "parts feature missing" and bounce (serkan's exact misread), instead of
+  // drilling in. Once any branch is visited the counts light up and the hint
+  // drops away on its own.
+  const treeCold =
+    !!categoryTree && categoryTree.length > 0 && categoryTree.every((c) => !c.partCount);
+
   const vehicleLabel: string = vehicle?.brandName
     ? `${vehicle.brandName}${cleanModelName(vehicle.model) ? ` ${cleanModelName(vehicle.model)}` : ""}`
     : t("vehicle.title");
@@ -305,6 +314,12 @@ function VehicleDetailPage() {
                 if (active) capture("catalog_search_opened", { vehicle_id: id });
               }}
             />
+            {!searchActive && !categoriesLoading && treeCold && (
+              <div className="mt-3 flex items-start gap-2 rounded-lg border border-border bg-muted/40 px-3 py-2.5 text-xs text-muted-foreground">
+                <Info className="mt-0.5 h-4 w-4 shrink-0 text-primary" />
+                <span>{t("vehicle.drillHint")}</span>
+              </div>
+            )}
           </div>
           {!searchActive &&
             (categoriesLoading ? (