First of all you have two controllers that map to /auth/register that return different things. If you are using spring thymeleaf, your login method in java should return the name of the template you are using for the login page. If I were you, on success of login I would have the button in html reference the success endpoint, which would go to your java endpoint.
<div>
<a th:href="@{/register/showStudentRegistrationForm}" class="btn btn-primary mt-3" role="button" aria-pressed="true">Register New Student</a>
</div>
For example something like this. If you have another question feel free to ask.