Customizing login error messages

I can’t see your complete code… However, your code should look like this:

function my_custom_error_messages( $error ) {
    global $errors;
    $err_codes = $errors->get_error_codes();
 
    // Invalid username.
    // Default: '<strong>ERROR</strong>: Invalid username. <a href="%s">Lost your password</a>?'
    if ( in_array( 'invalid_username', $err_codes ) ) {
        $error="<strong>ERROR</strong>: Wrong username.";
    }
 
    // Incorrect password.
    // Default: '<strong>ERROR</strong>: The password you entered for the username <strong>%1$s</strong> is incorrect. <a href="%2$s">Lost your password</a>?'
    if ( in_array( 'incorrect_password', $err_codes ) ) {
        $error="<strong>ERROR</strong>: Wrong password.";
    }
 
    return $error;
};
add_filter( 'login_errors', 'my_custom_error_messages' );

The code above has been tested and worked.