Is it possible to register a new template file?

I would strongly suggest you use a WordPress page template. At the top of dashboard.php:

<?php

/**
 * Template Name: Dashboard
 */

Now create a page called “Dashboard” and assign it the dashboard template.

This way you’re not loading WordPress yourself (nearly always bad) & WordPress & all your plugins will function as normal (creating custom endpoints in WordPress that don’t ultimately map to a loop/post object can hit a lot of problems as vast swathes of the frontend assume they do).