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/interface-adapters/controllers/sign-up.controller.test.ts

@@ -7,7 +7,7 @@ import { InputParseError } from "@/entities/errors/common";
 import { userFactory } from "@/__factories__/user.factory";
 
 describe("signUpController", () => {
-  it("creates a new user when passwords match", async () => {
+  it("returns a cookie on successful sign-up", async () => {
     const users = new MockUsersRepository([]);
     const auth = new MockAuthenticationService(users);
     const useCase = signUpUseCase(users, auth);
@@ -18,7 +18,8 @@ describe("signUpController", () => {
       password: "secret_password",
       confirmPassword: "secret_password",
     });
-    expect(result.user.username).toBe("carol");
+    expect(result.name).toBe("session");
+    expect(result.value).toBeTruthy();
   });
 
   it("throws InputParseError when passwords do not match", async () => {
@@ -39,7 +40,6 @@ describe("signUpController", () => {
   it("throws InputParseError when username is too short", async () => {
     const users = new MockUsersRepository([]);
     const auth = new MockAuthenticationService(users);
-    // Pre-seed so we don't hit the taken-username error
     await users.createUser(userFactory.build({ username: "alice" }));
     const useCase = signUpUseCase(users, auth);
     const controller = signUpController(useCase);