submitForm() isn't called
The code in the question is mixing three different types of templates:

Custom twig template in a controller
https://www.drupal.org/docs/theming-drupal/twig-in-drupal/create-custom-twig-templates-for-custom-module

Overriding form.html.twig
How to Create twig template files in drupal 8 for customizing user login,profile edit and forget password forms?

Adding a custom form template
How to render specific form elements from the *.theme file


The confusing part of your question is that you are using the same template reset-pasword.html.twig for 1. and 3.
The issue discussed in the comments about the special form elements applies only to 2.
You can use all three template levels at the same time. Then they are nested inside of each other which you see when you enable twig debugging.
More info Custom registration twig template.