What is the ruling on using the (siwāk) toothstick and toothpaste while fasting?

Shaykh Muqbil ibn Hādi al-Wādiʿī:

In regards to using the (siwāk) toothstick from the al-Arāk [tree] then there is no problem with it, even if it is green. As for using toothpaste, then we advise abandoning it in Ramaḍān, and we do not have any proof to say it nullifies the fast. So it is obligatory that he makes sure nothing enters his stomach.

Indeed the Prophet ﷺ said, “Sniff water into the nose excessively [in wudu], unless you are fasting.”