implement SignupUser use case

validates email present + format (wraps EmailAddress vo's
InvalidArgumentException as BadRequest), password present +
>= 8 chars, then ensures email not already registered. hashes
password through injected PasswordHasher and persists via
UserRepository->create with isAdmin=false (admins are seeder-
only per plan). throws DomainException on duplicate email so
the controller layer can map it to 409. all 18 tests pass.

backend/app/User/UseCases/SignupUser/SignupUser.php

@@ -0,0 +1,57 @@
+<?php
+
+namespace App\User\UseCases\SignupUser;
+
+use App\Auth\PasswordHasher;
+use App\Exceptions\BadRequestException;
+use App\Shared\ValueObject\EmailAddress;
+use App\User\CreateUserDto;
+use App\User\User;
+use App\User\UserRepository;
+use DomainException;
+use InvalidArgumentException;
+
+class SignupUser
+{
+    private const MIN_PASSWORD_LENGTH = 8;
+
+    public function __construct(
+        private UserRepository $userRepo,
+        private PasswordHasher $hasher,
+    ) {}
+
+    /**
+     * @throws BadRequestException
+     * @throws DomainException
+     */
+    public function execute(SignupUserRequest $request): User
+    {
+        if ($request->email === null || $request->email === '') {
+            throw new BadRequestException('email is required');
+        }
+        if ($request->password === null || $request->password === '') {
+            throw new BadRequestException('password is required');
+        }
+        if (strlen($request->password) < self::MIN_PASSWORD_LENGTH) {
+            throw new BadRequestException(
+                'password must be at least '.self::MIN_PASSWORD_LENGTH.' characters'
+            );
+        }
+
+        try {
+            $email = new EmailAddress($request->email);
+        } catch (InvalidArgumentException $exception) {
+            throw new BadRequestException($exception->getMessage());
+        }
+
+        if ($this->userRepo->findByEmail($email) !== null) {
+            throw new DomainException('email already registered');
+        }
+
+        return $this->userRepo->create(new CreateUserDto(
+            email: $email,
+            passwordHash: $this->hasher->hash($request->password),
+            isAdmin: false,
+        ));
+    }
+}

backend/app/User/UseCases/SignupUser/SignupUserRequest.php

@@ -0,0 +1,11 @@
+<?php
+
+namespace App\User\UseCases\SignupUser;
+
+class SignupUserRequest
+{
+    public function __construct(
+        public ?string $email,
+        public ?string $password,
+    ) {}
+}