Form Submit without module
Two ways to approach this.

One way is to use the Webform module. If this is just a simple contact form, you can get this done with Webform in five minutes.

The second way is create a custom module that implements a route, Form class and related methods. Wouldn't take an intermediate long, but a beginner should try Webform first.

You cannot simply paste form HTML into a twig file and expect it do anything. Drupal is ignorant to its existence and therefore no hooks will work, as you already saw.

https://www.drupal.org/project/webform