What is the meaning of "intentionally opening the mouth until dust enters the interior cavity (jawf) invalidates the fast," as stated by al-Nawawi in al-Majmu‘, and does it refer to intentionally not closing the mouth despite seeing dust, or intentionally causing dust to enter the mouth by opening it?

The fasting person does not break their fast if road dust reaches their throat, even if they sit in a dusty place and are able to close their mouth. If the fasting person intentionally opens their mouth and dust enters their throat, the soundest of the two opinions is that their fast is not invalidated. This is what scholars from the four schools of thought and others have agreed upon, because it is impossible to guard against dust and there is hardship in doing so.