Ignore "empty" fields when saving

First you need to catch the input then you can save it from $_POST So i assume your input fields names are myplugin_id , myplugin_api_key and myplugin_checkbox what you are currently doing is just going to replace the option with myplugin_checkbox

You can try

    function register_myplugin_settings() {
       if ( isset( $_POST['myplugin_id'] ) && ! empty( $_POST['myplugin_id'] ) ) {
          update_option( 'myplugin_id', sanitize_text_field( $_POST['myplugin_id'] ) );
       }
       if ( isset( $_POST['myplugin_api_key'] ) && ! empty( $_POST['myplugin_api_key'] ) ) {
          update_option( 'myplugin_api_key', sanitize_text_field( $_POST['myplugin_api_key'] ) );
       }
       if ( isset( $_POST['myplugin_checkbox'] ) && ! empty( $_POST['myplugin_checkbox'] ) ) {
          update_option( 'myplugin_checkbox', sanitize_text_field( $_POST['myplugin_checkbox'] ) );
       }
    }

update_option is straight to save the setting or option with its name. And to retrive data back from database you can use get_option function like

$myplugin_id = get_option( 'myplugin_id' );

if ( ! empty( $myplugin_id ) ) {
   //Dosomething when id is not empty
} else {
   //Do something when empty
}

If you still want to use the register_setting function just replace update_option with that one and check their documentation how to save the input there https://developer.wordpress.org/reference/functions/register_setting/

Good luck.

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