I saw the Messenger of Allah ﷺ using the tooth-stick while fasting on countless occasions, more than I could count or number.
حدثنا يحيى عن سفيان عن عاصم بن عبيد الله
رأيت رسول الله ﷺ يستاك ما لا أعد ولا أحصي وهو صائم
Its chain of transmission is hasan, mentioned previously at 15618.