Must one who needs to eat or drink on Tishe Beav only take the minimal measurements “Shiurim” as required on Yom Kippur?

Some Poskim^[1] rule one is required to follow the same eating and drinking measurements “Shiurim” prescribed on Yom Kippur. Other Poskim^[2] however rule it is not necessary. Practically, the custom is not to follow the former opinion, and hence one who is permitted to eat or drink may do so without limitation.^[3]

[1] Tzemach Tzedek O.C. 108:110; Divrei Nechemia 42; Sefer Haminhagim p. 92 [English]; Halachos Ketanos 2:100; Maharam Shick 289; Shaiy Lamorah 4; Marcheshes 1:14; Biur Halacha 554 “Bemakom” in name of Pischeiy Olam

[2] Chida in Machazik Bracha, brought in Kaf Hachaim 554:31; Maharam Shick 290; Avnei Nezer 540; Aruch Hashulchan 554:7

[3] Shevet Halevi 4:56; Kinyan Torah 1:118; Tzitz Eliezer 10:25-16; Shraga Hameir 1:59; Piskeiy Teshuvos 554:9; Hiskashrus 889 that so he received from several Rabbanei Anash, despite the ruling in Sefer Haminhagim ibid

The reason: Some suggest the entire reason behind the Shiurim recorded in the previous Poskim who are stringent is order to also gain the advantage of being considered to have fasted, and hence be able to count for a Minyan for Kerias Hatorah, and saying Aneinu and the like, however not that one is required to follow these Shiurim. [See Hiskashrus ibid; Piskeiy Teshuvos ibid and 566:6; Marcheshes ibid]