Python-Twilio is not sending sms with test credential.
Twilio developer evangelist here.
Test account credentials don't actually send SMS messages, they are test endpoints that let you know your HTTP calls are working as expected. That's why you have to use a specific number.
To test with the number you bought on your account you will need to use your real account credentials. Your Twilio trial account does come with some free credit to test these messages out before you need to upgrade, so I recommend changing to use those real credentials and the number you bought and you should start to see SMS messages coming through to your phone.
As a side note, the call to client.sms.messages.create
actually uses a deprecated API. You can update that to client.messages.create
and it will use the more modern Messages endpoint. (Side point on that though, the test credentials won't work at all with that endpoint, I still recommend using your real credentials and trial credit to test.)