feat(api): 관리자 카테고리 CRUD 추가 및 보드에 category 연동\nfeat(api): 공개 보드 목록 category 포함/필터 지원\ndocs(todo): 체크리스트 2.1~2.3 완료 표시

src/app/api/admin/categories/route.ts

@@ -0,0 +1,27 @@
+import { NextResponse } from "next/server";
+import prisma from "@/lib/prisma";
+import { z } from "zod";
+
+export async function GET() {
+  const categories = await prisma.boardCategory.findMany({
+    orderBy: [{ sortOrder: "asc" }, { createdAt: "asc" }],
+  });
+  return NextResponse.json({ categories });
+}
+
+const createSchema = z.object({
+  name: z.string().min(1),
+  slug: z.string().min(1),
+  sortOrder: z.coerce.number().int().optional(),
+  status: z.enum(["active", "hidden"]).optional(),
+});
+
+export async function POST(req: Request) {
+  const body = await req.json().catch(() => ({}));
+  const parsed = createSchema.safeParse(body);
+  if (!parsed.success) return NextResponse.json({ error: parsed.error.flatten() }, { status: 400 });
+  const category = await prisma.boardCategory.create({ data: parsed.data });
+  return NextResponse.json({ category }, { status: 201 });
+}
+
+