Yes, you can definitely do just what the Loom example has. You would create a folder, and put the page inside of it. Then, the URL to get to that page would just be website.com/folder/pagename
If you want a subdomain instead, such as pagename.website.com, that would then redirect to website.com/folder/pagename, you’d set up a redirect with your domain registrar so that when someone accesses the subdomain, it sends them to the page.
Neither of these scenarios would require an additional hosting plan.