The central debate about the Torah's injunction in this matter is around the phrase, "
וְעִנִּיתֶ֖ם אֶת נַפְשֹׁתֵיכֶ֑ם" which the CSB translates as "you shall practice self-denial." Secondary Jewish literature often interpreted this as fasting, and a summary of this and other issues concerning a Jewish version of fasting can be found here:
https://www.thetorah.com/article/why-jews-fast It is notable how the phrase, "denied ourselves" (CSB) is paralleled with the verb "fasted" in Isaiah 58:3, and appears to be a case of synonymous parallelism.
What is not debated, however, is that the people who were under the Mosaic Law frequently saw fasting as a natural outworking of their relationship to God. The above article's citation of Jud 20:26, 1 Sam 7:5, Ezr 8:21, Isa 58:3, etc.