Answer: There is a machlokes among the rishonim as to whether the rule ‘ein bishul achar bishul, something that has been cooked cannot be cooked again’, applies to liquids as well as solids. Rambam (Shabbos 9:3), Rashba (Shabbos 40b) and Ran (Shabbos 19a) write that it applies to liquids, too and so there would be no issur mideoraisa to reheat liquids (See Beis Yosef OC 318:4). The Shulchan Aruch (OC 318:4), however, follows Rashi (Shabbos 34a), Rabbeinu Yonah and the Rosh (Shabbos 3:11), who holds that reheating liquids is bishul (See Biur Halacha 318:4).
The Gemara (Kesubos 34a, Chullin 15a) writes that if one transgressed a melacha on Shabbos, there is a machlokes as to whether they or others can benefit from it on Shabbos or afterwards. The Gemara discusses whether this prohibition is mideoraisa or miderabanan. Rambam (Shabbos 6:23) and the Shulchan Aruch (OC 318:1) follow R’ Yehuda and write that if one accidentally cooked food on Shabbos, everyone must wait until after Shabbos to eat it. The Vilna Gaon (Biur Hagra, OC 318:1), however, follows Tosafos and others who pasken like R’ Meir, who holds that may one eat such food on Shabbos.
The Mishna Berura (318:7) writes that while we should generally follow the Shulchan Aruch on this, if necessary, one can rely on the Vilna Gaon. Thus, if this was one’s main dish for their Shabbos meal, one could still serve it.
The Pri Megadim (Eshel Avraham 318:10) and Mishna Berura (318:2) write that when there is a machlokes as to whether something is an issur or not, one doesn’t need to wait to benefit from it. Following the opinion in the Gemara that this prohibition against benefitting from forbidden melacha is miderabanan, we apply the rule of safek derabanan lekula, we are lenient in matters of Rabbinic doubt. As there are rishonim who maintain that ‘ein bishul achar bishul’ applies equally to liquids, one who accidentally reheated a liquid would not have to wait to eat it.
In conclusion, one may serve food containing liquid that was accidentally reheated on Shabbos.