Does the Hadith: "Whoever among you started the day fasting" include the Ramadan fast, or is it specific to voluntary fasts, and is there any recorded statement from scholars that explicitly mentions its inclusion of the obligatory Ramadan fast?

What Imam Ibn Rajab did concerning the hadith (definition) is correct, and he believes that the hadith includes the fasting of Ramadan (definition). This is indicated by his statement in "Lata'if al-Ma'arif": "The month of Ramadan is a month in which Allah bestows upon His servants mercy, forgiveness, and liberation from the Fire, especially on the Night of Qadr." He believes that combining fasting with charity is among the requisites for Paradise, citing the hadith: "Indeed, in Paradise there are chambers whose exteriors are visible from their interiors… for those who speak well, feed the poor, persist in fasting, and pray at night while people are asleep." These qualities are combined in Ramadan. This is supported by the superiority of obligatory acts over voluntary ones; if the reward is attained by one who fasts voluntarily and adds other deeds, it is even more so for one who fasts obligatorily. Therefore, the hadith includes both obligatory and voluntary fasting.