I’d try a simple wp_mail() snippet that will test if the wp_mail process is working properly:
wp_mail( '[email protected]', 'The subject', 'The message' );
I also saw a note in the wp_mail in WP Codex that some hosts will require a ‘[email protected]’ mail account created before it will send out the message.
Take a look at the dev pages here https://developer.wordpress.org/reference/functions/wp_mail/ . Note that you may need to set up the wp_mail_from() value to specify the ‘from’ address.
Also, when you send the test to your own email, check your spam/trash folders for interception.
Plus, of course, sanitizing the input from your form fields.