Build Advanced TypeScript Utility Types for Type-Safe Development

Create a comprehensive TypeScript utility types library for a [PROJECT_TYPE] project that enforces type safety across [DOMAIN_CONTEXT] (e.g., API responses, form handling, state management). **Utility Types to Implement:** 1. **API Layer Types**: - `ApiResponse<T>`: A discriminated union type with `success` and `error` variants, where the success variant contains `data: T` and the error variant contains `code: number` and `message: string` - `PaginatedResponse<T>`: Extends `ApiResponse` with `meta: { page, perPage, total, totalPages }` - `EndpointConfig<TParams, TBody, TResponse>`: Maps route parameters, request body, and response type for [NUMBER] endpoints: [ENDPOINT_LIST] 2. **Deep Manipulation Types**: - `DeepPartial<T>`: Recursively makes all properties optional - `DeepReadonly<T>`: Recursively makes all properties readonly - `DeepRequired<T>`: Recursively makes all properties required - `PathKeys<T>`: Extracts all valid dot-notation paths from a nested object type (e.g., `'user.address.city'`) - `PathValue<T, P>`: Resolves the type at a given dot-notation path 3. **Domain-Specific Types**: - `FormState<T>`: Maps each field of `T` to `{ value: T[K], error: string | null, touched: boolean, dirty: boolean }` - `StrictOmit<T, K>`: Like `Omit` but enforces that `K` must be actual keys of `T` - `RequireAtLeastOne<T, Keys>`: Ensures at least one of the specified keys is present - `MutuallyExclusive<T, K1, K2>`: Ensures only one of two property groups can exist 4. **Validation & Guards**: - Write type guard functions for each `ApiResponse` variant - Create a `assertNever(x: never)` exhaustiveness checker - Implement a `Brand<T, B>` type for nominal typing of [BRANDED_TYPES] (e.g., UserId, EmailAddress) For each utility type, provide: the implementation, a JSDoc comment explaining usage, and at least 2 test cases using `type-testing` patterns (Expect<Equal<...>>) to prove correctness.