All products are assigned to at least one category

Products without a category assignment become invisible to browsing and filtering — they exist in the database but can't be discovered through any navigation path other than direct search. Beyond UX, ISO 25010:2011 functional-correctness treats uncategorized products as broken catalog behavior: the product is present but unreachable. A nullable categoryId foreign key means every product creation path in the codebase can skip assignment, and there's no audit trail for which products were left uncategorized. At scale, this creates catalog rot: orphaned products accumulate, promotional campaigns miss items, and inventory counts diverge from what customers see.

Add a non-optional many-to-many relationship between Product and Category in prisma/schema.prisma, and enforce at least one category assignment in src/app/api/products/route.ts.

model Product {
  id         String     @id @default(cuid())
  name       String
  categories Category[]
}

model Category {
  id       String    @id @default(cuid())
  name     String
  products Product[]
}

In the product creation route, reject requests with an empty categories array:

if (!categoryIds || categoryIds.length === 0) {
  return Response.json({ error: 'At least one category is required' }, { status: 400 })
}