Hook into and send mail using WP Mail SMTP type plugin from HTML static front page?

You’re making it way more complicated than in needs to be.

WP Mail SMTP is a plugin that allows you to have WP’s wp_mail() function send through an SMTP account instead of relying on the web server.

You’re not, in this case, doing anything specific with WP Mail SMTP. What you’re going to do is use wp_mail() – and the result is generic, so it doesn’t matter whether you’re using WP Mail SMTP, some other plugin, or no plugin. It’s all the same.

So what you actually need to know is how to use wp_mail(), which is documented here. By virtue of the fact that you’re using WP Mail SMTP, anything you send through wp_mail() will be going through the account specified in the plugin.

Your question does lack some specifics in terms of what you’re doing specifically (i.e. how you expect your form to work) and also what you actually know how to do (do you know PHP? I assume you do). So, I’m going to answer the question you have and assume that you know how to get form $_POST results and also how to handle PHP for this.

Wherever you are posting your form to, if it’s a non-WP page, you’ll need to make sure need to make sure that WordPress is loaded in order to use the wp_mail() function to send your form results. So whether that’s the original page itself or another “thank_you” type page, either way it will need to be PHP.

<?php
// Not loading WP templates...
define( 'WP_USE_THEMES', false );

// Load WordPress Core (make sure the path is correct)
require_once( 'path/to/wp-load.php' );

// Assume you know how to check if the form is posted, so this is generic...
if ( $_POST ) {

    $to = '[email protected]';

    $subject="Someone sent you a message!";

    // Build the body based on your form...
    $name  = sanitize_text_field( $_POST['name'] );
    $email = sanitize_email( $_POST['email'] );
    $body  = sanitize_textarea( $_POST['message'] );

    $message = "Someone filled out your form as follows: \r\n\r\n";
    $message.= "name: $name \r\n";
    $message.= "email: $email \r\rn";
    $message.= "the message: \r\n";
    $message.= $body;

    // Send the message...
    wp_mail( $to, $subject, $message );

}