refactor(auth): unify use-case I/O schemas + presenter + feature error map

Per Plan 9 (spec R1-R28):
- Use cases: input + output schemas (signIn, signUp); input-only for
  signOut (void output). Use case body validates output via
  outputSchema.parse before returning.
- Controllers: receive `unknown`; safeParse with the use-case schema;
  presenter (returning cookie) for signIn/signUp; void return for
  signOut.
- New integrations/api/procedures.ts with authProcedure built via
  defineErrorMiddleware([[InputParseError,"BAD_REQUEST"],
  [AuthenticationError,"UNAUTHORIZED"], [UnauthenticatedError,
  "UNAUTHORIZED"], [UnauthorizedError,"FORBIDDEN"]]).
- Router uses authProcedure + .input(xInputSchema) for every procedure.
- src/index.ts exports schemas + types + IUseCase/IController aliases.
- package.json gains ./ui subpath; src/ui/index.ts placeholder
  (auth has no query builders today).
- New tests: R25 output-validation per use case (signIn, signUp);
  R26 router error-mapping (UNAUTHORIZED on missing user,
  BAD_REQUEST on schema fail).

Refactor log: §1, §2, §3.1, §3.2, §3.3, §5.1, §5.2, §6.1, §6.2
Spec: R1–R6, R8–R15, R18, R19, R22–R26

packages/auth/src/application/use-cases/sign-up.use-case.ts

@@ -1,10 +1,33 @@
+import { z } from "zod";
+
 import { AuthenticationError } from "../../entities/errors/auth";
-import type { Cookie } from "../../entities/models/cookie";
-import type { Session } from "../../entities/models/session";
-import type { User } from "../../entities/models/user";
+import { cookieSchema } from "../../entities/models/cookie";
+import { sessionSchema } from "../../entities/models/session";
 import type { IUsersRepository } from "../repositories/users.repository.interface";
 import type { IAuthenticationService } from "../services/authentication.service.interface";
 
+// ── Input ────────────────────────────────────────────────────────────────
+export const signUpInputSchema = z
+  .object({
+    username: z.string().min(3).max(31),
+    password: z.string().min(6).max(255),
+    confirmPassword: z.string().min(6).max(255),
+  })
+  .strict()
+  .refine((d) => d.password === d.confirmPassword, {
+    message: "Passwords do not match",
+    path: ["confirmPassword"],
+  });
+export type SignUpInput = z.infer<typeof signUpInputSchema>;
+
+// ── Output ───────────────────────────────────────────────────────────────
+export const signUpOutputSchema = z.object({
+  session: sessionSchema,
+  cookie: cookieSchema,
+});
+export type SignUpOutput = z.infer<typeof signUpOutputSchema>;
+
+// ── Use case ─────────────────────────────────────────────────────────────
 export type ISignUpUseCase = ReturnType<typeof signUpUseCase>;
 
 export const signUpUseCase =
@@ -12,14 +35,7 @@ export const signUpUseCase =
     usersRepository: IUsersRepository,
     authenticationService: IAuthenticationService,
   ) =>
-  async (input: {
-    username: string;
-    password: string;
-  }): Promise<{
-    session: Session;
-    cookie: Cookie;
-    user: Pick<User, "id" | "username">;
-  }> => {
+  async (input: SignUpInput): Promise<SignUpOutput> => {
     const existingUser = await usersRepository.getUserByUsername(input.username);
     if (existingUser) {
       throw new AuthenticationError("Username taken");
@@ -36,9 +52,5 @@ export const signUpUseCase =
 
     const { cookie, session } = await authenticationService.createSession(newUser);
 
-    return {
-      cookie,
-      session,
-      user: { id: newUser.id, username: newUser.username },
-    };
+    return signUpOutputSchema.parse({ session, cookie });
   };