Does “Sucking” Count as Drinking or Eating?

In my humble opinion, the explanation is straightforward. With regard to the laws of Shabbat, the issue is whether this is considered the melachah of squeezing or not. Thus, the expression “the manner of eating” does not exclude the fact that it is drinking; rather, it merely defines that this is not a melachah. As we find with other melachot, anything done in the manner of eating is not included in the prohibition of melachah. For example, selecting food from waste for immediate use is permitted because it is “the manner of eating,” as written in Chazon Ovadia, vol. 4, p. 108. Certainly, the intent there is not that the act of selecting food from waste is actual eating for purposes of blessings, such that one would recite a blessing over that act. Rather, anything that is a “manner” of eating is not a melachah. The same applies here: it is a “manner” of eating even though it is drinking. Although, when the grapes are outside the mouth, Chazon Ovadia, which you cited, wrote that it is proper to be stringent in accordance with the opinion of the Yere’im, no. 120, Orchot Chaim, Hilchot Shabbat, no. 19, and those who agree with them, may their memory be blessed, this is because they maintain that if the grapes are not in the mouth and one sucks them by suction, this is “the manner of squeezing,” and is unlike an act of eating or drinking, which is the ordinary manner of people.

In contrast, regarding the laws of blessings, where the question is whether this is “eating” as opposed to “drinking,” Maran Rabbi Ovadia Yosef zt”l wrote in Shu”t Yabia Omer, vol. 8, Orach Chaim no. 25, section 6, that one should be concerned that if one sucks a solid into his mouth in a manner that he swallows it while liquid, it is considered drinking rather than eating. Consider this carefully.