feat(finance): Phase 6 — Budget & Analytics

Add monthly budgets per category with spend-vs-budget dashboard and 6-month trend table.
Includes upsert budget API, monthly analytics endpoint, inline budget editing, and route auth fixes.

src/app/api/budgets/[id]/route.ts

@@ -0,0 +1,18 @@
+import { NextRequest, NextResponse } from "next/server";
+import { getCurrentUser } from "@/lib/auth";
+import { queryRaw } from "@/lib/db";
+
+export async function DELETE(req: NextRequest, { params }: { params: Promise<{ id: string }> }) {
+  const user = await getCurrentUser(req);
+  if (!user) return NextResponse.json({ error: "Unauthorized" }, { status: 403 });
+
+  const { id } = await params;
+  const existing = await queryRaw<{ id: number }>(
+    `SELECT id FROM budgets WHERE id = $1 AND owner_id = $2`,
+    [Number(id), user.id]
+  );
+  if (!existing.length) return NextResponse.json({ error: "Not found" }, { status: 404 });
+
+  await queryRaw(`DELETE FROM budgets WHERE id = $1`, [Number(id)]);
+  return NextResponse.json({ ok: true });
+}