Is abstaining from food before the dawn athan an innovation (bid'ah), based on the hadiths concerning drinking the vessel upon hearing the call?

It is not permissible to continue eating and drinking after hearing the second Fajr adhan (definition), because the muezzin usually calls the adhan at the break of dawn, based on the Almighty's saying: "And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]. Then complete the fast until the nightfall." And based on the Prophet's (peace be upon him) saying: "Indeed, Bilal calls the adhan at night, so eat and drink until Ibn Umm Maktum calls the adhan." As for abstaining before Fajr, it is not an innovation; rather, it is permissible, as some of the Companions used to abstain before Fajr.