Peace be upon you.
Ayatollah al-Uzma Sayyid Sistani (may Allah protect him):
Brushing teeth with a toothbrush and toothpaste is not among the things that invalidate the fast, as long as the fasting person does not swallow anything that mixes with their saliva during the cleaning process. A small amount that is consumed with saliva does not harm the fast.
Ayatollah al-Uzma Sayyid Khamenei (may Allah protect him):
It is permissible to use a toothbrush and toothpaste, as well as a miswak, to clean the teeth, provided that nothing is swallowed, even if one feels the taste in their mouth.
May you be successful in all good.