Why is my form going to frontend on html form submission present on the php files inside my custom plugin?

Add a new URL using add_submenu_page (without any parent assigned) and post your form data on that URL. Refer to this page for adding sub-menu page.

Also, you should not send form data on any PHP file like this. This, will opens up your plugin for external attacks.

Let, know if you unable to figure out the way of doint this.

Have a Good Day!