Login Api with Meta_key and Meta_value

To log a user in you really only need the user’s ID. Based on your info you should be able to obtain it from the username field.

// Get User object
$user = get_user_by( 'login', $username );

// Clear any auth cookies
wp_clear_auth_cookie();

// Log the user in
wp_set_current_user( $user->ID );
wp_set_auth_cookie( $user->ID );

On a non-login page you could probably refresh right after;

header("Refresh:0");
exit();

Now that the hard part is out of the way, it comes down to where you’re getting your username from.

Most people don’t store username/password in plaintext on post_metadata. But even then, and you’re making a whole loop query for login data, you’re still going to have to settle on logging in a single user. So the whole $data['result'][]= doesn’t make a lot of sense.