To send messages to countries other than the one you registered with, you need to enable SMS Geo Permissions in your Twilio account. By default, Twilio restricts SMS sending to the country used during sign-up.
You still need this if you use a Messaging Service. Geo Permissions decide which countries Twilio delivers to. A Messaging Service decides which of your numbers sends the message. They do different jobs, you usually need both for multi-region SMS.
Review this Twilio help article to enable this Twilio SMS Geo Permissions
If you continue to have issues after enabling the permissions, please contact the Twilio support team for account review and resolution: Contact Twilio Support